Wireless-Powered Communication Networks: Architectures, Protocols, and Applications 1107135699, 9781107135697

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Cambridge University Press 978-1-107-13569-7 — Wireless-Powered Communication Networks Edited by Dusit Niyato , Ekram Hossain , Dong In Kim , Vijay Bhargava , Lotfollah Shafai Frontmatter More Information

Wireless-Powered Communication Networks Architectures, Protocols, and Applications Learn the fundamentals of architecture design, protocol optimization, and application development for wireless-powered communication networks with this authoritative guide. You will gain a detailed understanding of the issues surrounding architecture and protocol design, with key topics covered including relay-based energy harvesting systems, multiple-antenna systems for simultaneous wireless information and power transfer (SWIPT), performance modeling and analysis, and ambient wireless energyharvesting-based cellular systems. Current applications of energy harvesting and transfer in different wireless networking scenarios are discussed, helping you to understand practical system development and implementation issues from an engineering perspective. The first book to provide a unified view of energy harvesting and wireless power transfer networks from a communications perspective, this is an essential text for researchers working on wireless communication networks and wireless systems, RF engineers, and wireless application developers. Dusit Niyato is an Associate Professor in the School of Computer Science and Engineering at Nanyang Technological University, Singapore. He is the recipient of the IEEE Communications Society Asia Pacific Best Young Researcher Award and the IEEE Communications Society Fred W. Ellersick Prize Paper Award. Ekram Hossain is a Professor in the Department of Electrical and Computer Engineering at the University of Manitoba, Canada, and a Fellow of the IEEE. He is the co-editor or -author of several books, including Wireless Device-to-Device Communications and Networks (Cambridge, 2015) and Cooperative Cellular Wireless Networks (Cambridge, 2011). Dong In Kim is a Professor in the School of Information and Communication Engineering at Sungkyunkwan University Korea. He previously served as the Founding Editorin-Chief for the IEEE Wireless Communications Letters (2012–2015), and in 2014 was the first recipient of the ERC Excellence Award in Wireless Communications from the National Research Foundation of Korea Vijay Bhargava is a Professor in the Department of Electrical and Computer Engineering at the University of British Columbia, Canada, where he is currently leading a major research program in 5G Wireless Systems. His previous positions include President of the IEEE’s Information Theory and Communications Societies, and Editor-in-Chief of the IEEE Transactions on Wireless Communications. Lotfollah Shafai is a Distinguished Professor Emeritus in the Department of Electrical and Computer Engineering at the University of Manitoba, Canada. His numerous awards and recognitions include the Canada Council for the Arts Killam Prize in Engineering (2011), and the IEEE Chen-To-Tai Distinguished Educator Award (2009). He was also a Canada Research Chair in Applied Electromagnetics (2001–2015).

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Cambridge University Press 978-1-107-13569-7 — Wireless-Powered Communication Networks Edited by Dusit Niyato , Ekram Hossain , Dong In Kim , Vijay Bhargava , Lotfollah Shafai Frontmatter More Information

“This is a brilliant piece of work which provides a holistic view of the emerging energy harvesting-based wireless communications and networking technology. Starting with the basics . . . , the book cohesively covers different aspects of this technology, including circuit and antenna design issues for wireless energy harvesting devices and performance modeling and analysis of wireless energy harvesting and transfer-based wireless networks, as well as applications of this technology in different wireless networking scenarios. Standardization activities on wireless energy harvesting and transfer are also discussed. As a valuable addition to the library of graduate students, researchers and practitioners working in this area, this book will equip them for further reading and research on this exciting technology.” Vahid Tarokh, Harvard University “Wireless power transfer and energy harvesting networks have received tremendous attention in both the research community and industry recently . . . This book contains a comprehensive review of the various topics which are nicely organised and blended in a coherent manner. It will be an excellent introductory text to get into this exciting new topic of research.” Vincent Lau, Hong Kong University of Science and Technology

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Cambridge University Press 978-1-107-13569-7 — Wireless-Powered Communication Networks Edited by Dusit Niyato , Ekram Hossain , Dong In Kim , Vijay Bhargava , Lotfollah Shafai Frontmatter More Information

Wireless-Powered Communication Networks Architectures, Protocols, and Applications D U S I T N I YAT O Nanyang Technological University, Singapore

EKRAM HOSSAIN University of Manitoba, Canada

DONG IN KIM Sungkyunkwan University, Korea

V I J AY B H A R G AVA University of British Columbia, Canada

L O T F O L L A H S H A FA I University of Manitoba, Canada

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Cambridge University Press 978-1-107-13569-7 — Wireless-Powered Communication Networks Edited by Dusit Niyato , Ekram Hossain , Dong In Kim , Vijay Bhargava , Lotfollah Shafai Frontmatter More Information

University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 4843/24, 2nd Floor, Ansari Road, Daryaganj, Delhi – 110002, India 79 Anson Road, #06–04/06, Singapore 079906 Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107135697 © Cambridge University Press 2017 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2017 Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall A catalog record for this publication is available from the British Library Library of Congress Cataloging-in-Publication data Names: Niyato, Dusit, editor author. Title: Wireless-powered communication networks : architectures, protocols, and applications / [edited by] Dusit Niyato, Nanyang Technological University, Ekram Hossain, University of Manitoba, Dong In Kim, Sungkyunkwan University, Korea, Vijay Bhargava, University of British Columbia, Lotfollah Shafai, University of Manitoba, Canada. Description: Cambridge, United Kingdom : Cambridge University Press, 2017. | Includes bibliographical references and index. Identifiers: LCCN 2016021099 | ISBN 9781107135697 (Hardback) Subjects: LCSH: Wireless communication systems–Power supply. | Electromagnetic induction. | Microharvesters (Electronics) | Computer network architectures. | Computer network protocols. Classification: LCC TK5103.2 .W574126 2017 | DDC 004.6–dc23 LC record available at https://lccn.loc.gov/2016021099 ISBN 978-1-107-13569-7 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

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Contents

page ix xi

List of contributors Preface

Part I Basics of Wireless Energy Harvesting and Transfer Technology

1

1

3

Basics of Wireless Energy Harvesting and Transfer Dusit Niyato, Ekram Hossain, and Xiao Lu

2

1.1 Introduction 1.2 History of Wireless Energy Harvesting and Transfer Technology 1.3 Wireless Energy Harvesting and Transfer Technology 1.4 Wireless-Powered Communication Networks 1.5 International Standards 1.6 Implementation Examples 1.7 Summary References

3 5 7 17 20 31 36 36

Circuit Design for Wireless Energy Harvesting

44

Min Jae Kim, Kae Won Choi, Dong In Kim, Youngoo Yang, Kang Yoon Lee, and Keum Cheol Hwang

3

2.1 Introduction 2.2 Test-Beds for Long- and Short-Range RF Energy Harvesting Systems 2.3 Stored Energy Evolution Model for an IoT Sensor Node with Wireless Energy Harvesting Capability 2.4 Summary References

44 45

Antennas for Wireless Energy Harvesting and Massive MIMO Applications

86

74 84 85

Zahra A. Pour, Lotfollah Shafai, Ali M. Mehrabani, and Navid Rezazadeh

3.1 3.2 3.3 3.4 3.5

Introduction Historical Overview on Wireless Power Transmission Wireless Power Transmission Techniques Block Diagram of RF Wireless Power Transmission Candidate Antennas

86 87 89 92 93 v

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vi

Contents

3.6 Universal Design Examples: Slotted Microstrip Patch Antennas 3.7 Wideband Diversity Antennas 3.8 Design III: Wideband Dual-Diversity Antenna 3.9 Antennas for Massive-MIMO Applications 3.10 Summary References

103 109 114 123 126 127

Part II Architectures, Protocols, and Performance Analysis

133

4

135

Cooperative Networks with Wireless Energy Harvesting Sudha Lohani, Roya Arab Loodaricheh, Shankhanaad Mallick, Ekram Hossain, and Vijay Bhargava

5

4.1 Introduction 4.2 Relay-Based Energy Harvesting Systems 4.3 Relay Operation Policy 4.4 Resource Allocation 4.5 Open Issues and Challenges 4.6 Summary References

135 137 139 146 164 166 167

Multiple Antennas and Beamforming for SWIPT Systems

170

Derrick Wing Kwan Ng, Shiyang Leng, and Robert Schober

6

5.1 Introduction 5.2 System Model 5.3 Single-Objective Optimization 5.4 Multi-Objective SWIPT Optimization 5.5 Secure Communications in SWIPT Systems 5.6 Research Challenges 5.7 Summary 5.8 Appendix References

170 174 174 190 199 207 209 209 212

Backscattering Wireless-Powered Communications

217

Dinh Thai Hoang

6.1 Introduction 6.2 Application of Backscattering Communication in Wireless-Powered Body Area Networks 6.3 Future Research Directions 6.4 Summary 6.5 Appendix References

217 222 240 241 242 244

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Cambridge University Press 978-1-107-13569-7 — Wireless-Powered Communication Networks Edited by Dusit Niyato , Ekram Hossain , Dong In Kim , Vijay Bhargava , Lotfollah Shafai Frontmatter More Information

Contents

7

Dedicated Wireless Energy Harvesting in Cellular Networks: Performance Modeling and Analysis

vii

246

Hina Tabassum and Ekram Hossain

7.1 Introduction 7.2 Major Challenges in Dedicated Wireless Energy Harvesting 7.3 Centralized and Decentralized Dedicated WEH Architectures: Comparative Analysis 7.4 Numerical Results and Discussion 7.5 Summary References 8

246 247 250 258 261 263

Ambient Wireless Energy Harvesting in Small Cell Networks: Performance Modeling and Analysis

265

Ahmed Hamdi Sakr, Hina Tabassum, and Ekram Hossain

8.1 Introduction 8.2 Challenges in Ambient Wireless Energy Harvesting in Small Cell Networks 8.3 RF Ambient Energy Harvesting: Literature Review 8.4 Ambient Energy Harvesting: Network Performance Modeling and Analysis 8.5 Discussion 8.6 Uplink Coverage Probability 8.7 Numerical Results and Discussion 8.8 Summary References

265 266 268 271 277 280 281 286 286

Part III Applications of Wireless Energy Harvesting and Transfer

289

9

291

Sensor Networks with Wireless Energy Harvesting Xiao Lu

10

9.1 Introduction 9.2 Static Wireless Charger Deployment 9.3 Mobile Sensor Charger Optimization 9.4 Hardware Designs for Sensor Nodes with Wireless Energy Harvesting 9.5 Energy Scheduling in Wireless-Powered Sensor Networks 9.6 Future Research Directions 9.7 Summary References

291 291 298 309 311 326 329 329

Cognitive Radio Networks with Wireless Energy Harvesting

338

Dinh Thai Hoang

10.1 Introduction 10.2 Opportunistic Channel Access for RF-powered Cognitive Radio Networks

338 343

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11

Contents

10.3 Performance Optimization for Cooperative Multiuser Cognitive Radio Networks with RF Energy Harvesting Capability 10.4 Performance Optimization for Wireless-Powered Cognitive Radio Networks under Smart Jamming Attacks 10.5 Future Research Directions 10.6 Summary References

368 379 380 381

Mobile Ad-Hoc Networks and Delay-Tolerant Networks With Wireless Energy Harvesting

383

355

Dusit Niyato

11.1 Introduction 11.2 Basics of MANETs and DTNs 11.3 Cooperation in DTNs 11.4 Delay-Limited Communication in MANETs 11.5 Mobile Energy Sharing 11.6 Future Research Directions 11.7 Summary References

383 384 389 403 413 424 425 426

Index

430

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Cambridge University Press 978-1-107-13569-7 — Wireless-Powered Communication Networks Edited by Dusit Niyato , Ekram Hossain , Dong In Kim , Vijay Bhargava , Lotfollah Shafai Frontmatter More Information

Contributors

Vijay Bhargava University of British Columbia, Vancouver, BC, Canada Kae Won Choi Sungkyunkwan University, Korea Dinh Thai Hoang Nanyang Technological University, Singapore Ekram Hossain University of Manitoba, Winnipeg, MB, Canada Keum Cheol Hwang Sungkyunkwan University, Korea Dong In Kim Sungkyunkwan University, Korea Min Jae Kim Sungkyankwan University, Korea Kang Yoon Lee Sungkyunkwan University, Korea Shiyang Leng The Pennsylvania State University, USA Sudha Lohani University of British Columbia, Vancouver, BC, Canada Roya Arab Loodaricheh 314-2730 Acadia Road, Vancouver, BC, Canada

ix

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x

List of contributors

Xiao Lu University of Alberta, AB, Canada Shankhanaad Mallick 110-8738 French Street, Vancouver, BC, Canada Ali M. Mehrabani University of Manitoba, Winnipeg, MB, Canada Derrick Wing Kwan Ng University of New South Wales, Sydney, Australia Dusit Niyato Nanyang Technological University, Singapore Zahra A. Pour University of Alabama at Huntsville, Huntsville, AL, USA Navid Rezazadeh University of Manitoba, Winnipeg, MB, Canada Ahmed Hamdi Sakr University of Monitoba, Winnipeg, MB, Canada Robert Schober Friedrich-Alexander-Universität Erlangen–Nürnberg, Erlangen, Germany Lotfollah Shafai University of Manitoba, Winnipeg, MB, Canada Hina Tabassum University of Manitoba, Winnipeg, MB, Canada Youngoo Ynag Sungkyunkwan University, Korea

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Preface

Recently, there has been an upsurge of research interest in wireless-powered communication networks. These networks are based on energy harvesting and/or energy transfer technology, for mobile devices using wireless propagation media. This technology offers the capability of using different types of wireless medium, such as radio frequency and magnetic induction, to carry energy from dedicated sources to wireless nodes or to harvest energy from ambient sources. Therefore, this has become a promising solution to power energy-constrained wireless networks. Conventionally, energyconstrained wireless networks such as wireless sensor networks have a limited lifetime, which leads to significant deterioration in network performance and usability. By contrast, a network with wireless energy harvesting and transfer capability can be powered without using a fixed power supply. For example, it can harvest energy from environmental sources such as solar and wind energy or from other dedicated or nondedicated sources which are tetherless. Hence, there is no need to charge or replace the batteries physically, which can improve the flexibility and availability of the network substantially. Wireless energy has many advantages over other energy sources, including indoor support and stable and more predictable supply. There are three major types of wireless energy harvesting and transfer technique, namely, radio frequency (RF), inductive coupling, and magnetic resonance coupling techniques. In RF energy harvesting, radio signals with frequencies in the range from 3 kHz to 300 GHz are used as a medium to carry energy in the form of electromagnetic radiation. Inductive coupling is based on magnetic coupling that delivers electrical energy between two coils tuned to resonate at the same frequency. The electric power is carried through the magnetic field between two coils. Magnetic resonance coupling utilizes evanescent-wave coupling to generate and transfer electrical energy between two resonators. The resonator is formed by adding a capacitance on an induction coil. Inductive coupling and magnetic resonance coupling are near-field wireless transmission techniques featuring high power density and conversion efficiency. By contrast, RF energy transfer can be regarded as a far-field energy transfer technique. It is suitable for powering a larger number of devices distributed over a wide area. Wireless energy harvesting and transfer have found many applications and have recently been implemented in many devices, including mobile phones, healthcare devices, sensors, and RFID tags. With the increasing number of applications of RF energy harvesting/charging, the Wireless Power Consortium is also making efforts toward establishing an international standard for RF energy harvesting and transfer technology. xi

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Cambridge University Press 978-1-107-13569-7 — Wireless-Powered Communication Networks Edited by Dusit Niyato , Ekram Hossain , Dong In Kim , Vijay Bhargava , Lotfollah Shafai Frontmatter More Information

xii

Preface

Although wireless energy harvesting and transfer can be adopted in different types of wireless network, such as wireless sensor networks, mobile ad-hoc networks, and delaytolerant networks, to provide the power supply for the wireless nodes, it introduces many challenges. Unlike other forms of energy harvesting, e.g., wind, solar, and vibration, the efficiency of wireless energy harvesting and transfer depends on the relative distances between the energy sources and the harvesting devices of the wireless nodes. Therefore, the locations or placements as well as the density of power sources become a significant architectural issue for such networks. Moreover, with dedicated power sources in a wireless network, issues such as scheduling of users for energy transfer (or charging) as well as data transfer and transmission scheduling of data packets in the energy harvesting wireless nodes become important. Efficient usage of the harvested energy depends on the communication protocols used by these devices as well as other network nodes such as the base stations. Therefore, the schemes and solutions developed for traditional wireless communication networks without or with other forms of energy harvesting have to be revisited. They have to be redesigned and developed to meet the unique challenges that arise due to the distinctive nature of wireless energy harvesting and transfer. This book entitled Wireless-Powered Communication Networks: Architectures, Protocols, and Applications provides a comprehensive treatment of the latest research and technological developments concerning the architectures, protocols, and applications of networks with wireless energy harvesting and transfer capability. It is divided into three parts: Basics of Wireless Energy Harvesting and Transfer Technology (Part I), Architectures, Protocols, and Performance Analysis (Part II), and Applications of Wireless Energy Harvesting and Transfer (Part III). It starts with an introduction to the circuit and antenna design of wireless energy harvesting and transfer devices as well as the standardization efforts toward wireless energy transfer and harvesting technology (Part I). Then, in Part II, the book deals with several issues related to architecture and protocol design for networks with wireless energy harvesting and transfer capability. The topics covered in this part include relay-based energy harvesting systems and the related radio resource management issues, multiple antenna systems for simultaneous wireless information and power transfer (SWIPT), backscattering wireless-powered communications systems, and performance modeling and analysis of dedicated wireless energy harvesting as well as ambient wireless energy harvesting-based cellular systems. Part III of the book deals with applications of energy harvesting and transfer in different wireless networking scenarios, including those in sensor networks, cognitive radio networks, and mobile ad-hoc and delay-tolerant networks. In addition to reviewing the existing approaches for design and operation of energy harvesting wireless networks, the book also outlines the open issues and research challenges in this emerging area which will need to be explored by researchers. The book provides the following. • •

Background on wireless energy harvesting and transfer for RF, inductive coupling, and magnetic resonant coupling methods; Introduction to the circuit and antenna design issues for energy-harvesting devices;

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Cambridge University Press 978-1-107-13569-7 — Wireless-Powered Communication Networks Edited by Dusit Niyato , Ekram Hossain , Dong In Kim , Vijay Bhargava , Lotfollah Shafai Frontmatter More Information

Preface

•

• • • •

xiii

Reviews of several important network architecture and protocol design issues and performance analysis models for wireless energy harvesting and transfer-based wireless networks; Applications of wireless energy harvesting and transfer in different wireless networking scenarios; Standardization activities on wireless energy harvesting and transfer; A comprehensive list of references on topics related to wireless energy harvesting and transfer technology; Potential research directions.

We would like to acknowledge various grant-awarding agencies that supported part of the work reported in this book. These agencies include the Natural Sciences and Engineering Research Council of Canada (NSERC), the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2014R1A5A1011478) and Singapore MOE Tier 1 (RG18/13 and RG33/12) and MOE Tier 2 (MOE2014-T22-015 ARC 4/15).

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Preface

Recently, there has been an upsurge of research interest in wireless-powered communication networks. These networks are based on energy harvesting and/or energy transfer technology, for mobile devices using wireless propagation media. This technology offers the capability of using different types of wireless medium, such as radio frequency and magnetic induction, to carry energy from dedicated sources to wireless nodes or to harvest energy from ambient sources. Therefore, this has become a promising solution to power energy-constrained wireless networks. Conventionally, energyconstrained wireless networks such as wireless sensor networks have a limited lifetime, which leads to significant deterioration in network performance and usability. By contrast, a network with wireless energy harvesting and transfer capability can be powered without using a fixed power supply. For example, it can harvest energy from environmental sources such as solar and wind energy or from other dedicated or nondedicated sources which are tetherless. Hence, there is no need to charge or replace the batteries physically, which can improve the flexibility and availability of the network substantially. Wireless energy has many advantages over other energy sources, including indoor support and stable and more predictable supply. There are three major types of wireless energy harvesting and transfer technique, namely, radio frequency (RF), inductive coupling, and magnetic resonance coupling techniques. In RF energy harvesting, radio signals with frequencies in the range from 3 kHz to 300 GHz are used as a medium to carry energy in the form of electromagnetic radiation. Inductive coupling is based on magnetic coupling that delivers electrical energy between two coils tuned to resonate at the same frequency. The electric power is carried through the magnetic field between two coils. Magnetic resonance coupling utilizes evanescent-wave coupling to generate and transfer electrical energy between two resonators. The resonator is formed by adding a capacitance on an induction coil. Inductive coupling and magnetic resonance coupling are near-field wireless transmission techniques featuring high power density and conversion efficiency. By contrast, RF energy transfer can be regarded as a far-field energy transfer technique. It is suitable for powering a larger number of devices distributed over a wide area. Wireless energy harvesting and transfer have found many applications and have recently been implemented in many devices, including mobile phones, healthcare devices, sensors, and RFID tags. With the increasing number of applications of RF energy harvesting/charging, the Wireless Power Consortium is also making efforts toward establishing an international standard for RF energy harvesting and transfer technology. xi Downloaded from https:/www.cambridge.org/core. Columbia University Libraries, on 12 Jun 2017 at 22:27:40, subject to the Cambridge Core terms of use, available at .001

xii

Preface

Although wireless energy harvesting and transfer can be adopted in different types of wireless network, such as wireless sensor networks, mobile ad-hoc networks, and delaytolerant networks, to provide the power supply for the wireless nodes, it introduces many challenges. Unlike other forms of energy harvesting, e.g., wind, solar, and vibration, the efficiency of wireless energy harvesting and transfer depends on the relative distances between the energy sources and the harvesting devices of the wireless nodes. Therefore, the locations or placements as well as the density of power sources become a significant architectural issue for such networks. Moreover, with dedicated power sources in a wireless network, issues such as scheduling of users for energy transfer (or charging) as well as data transfer and transmission scheduling of data packets in the energy harvesting wireless nodes become important. Efficient usage of the harvested energy depends on the communication protocols used by these devices as well as other network nodes such as the base stations. Therefore, the schemes and solutions developed for traditional wireless communication networks without or with other forms of energy harvesting have to be revisited. They have to be redesigned and developed to meet the unique challenges that arise due to the distinctive nature of wireless energy harvesting and transfer. This book entitled Wireless-Powered Communication Networks: Architectures, Protocols, and Applications provides a comprehensive treatment of the latest research and technological developments concerning the architectures, protocols, and applications of networks with wireless energy harvesting and transfer capability. It is divided into three parts: Basics of Wireless Energy Harvesting and Transfer Technology (Part I), Architectures, Protocols, and Performance Analysis (Part II), and Applications of Wireless Energy Harvesting and Transfer (Part III). It starts with an introduction to the circuit and antenna design of wireless energy harvesting and transfer devices as well as the standardization efforts toward wireless energy transfer and harvesting technology (Part I). Then, in Part II, the book deals with several issues related to architecture and protocol design for networks with wireless energy harvesting and transfer capability. The topics covered in this part include relay-based energy harvesting systems and the related radio resource management issues, multiple antenna systems for simultaneous wireless information and power transfer (SWIPT), backscattering wireless-powered communications systems, and performance modeling and analysis of dedicated wireless energy harvesting as well as ambient wireless energy harvesting-based cellular systems. Part III of the book deals with applications of energy harvesting and transfer in different wireless networking scenarios, including those in sensor networks, cognitive radio networks, and mobile ad-hoc and delay-tolerant networks. In addition to reviewing the existing approaches for design and operation of energy harvesting wireless networks, the book also outlines the open issues and research challenges in this emerging area which will need to be explored by researchers. The book provides the following. • •

Background on wireless energy harvesting and transfer for RF, inductive coupling, and magnetic resonant coupling methods; Introduction to the circuit and antenna design issues for energy-harvesting devices;

Downloaded from https:/www.cambridge.org/core. Columbia University Libraries, on 12 Jun 2017 at 22:27:40, subject to the Cambridge Core terms of use, available at .001

Preface

•

• • • •

xiii

Reviews of several important network architecture and protocol design issues and performance analysis models for wireless energy harvesting and transfer-based wireless networks; Applications of wireless energy harvesting and transfer in different wireless networking scenarios; Standardization activities on wireless energy harvesting and transfer; A comprehensive list of references on topics related to wireless energy harvesting and transfer technology; Potential research directions.

We would like to acknowledge various grant-awarding agencies that supported part of the work reported in this book. These agencies include the Natural Sciences and Engineering Research Council of Canada (NSERC), the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2014R1A5A1011478) and Singapore MOE Tier 1 (RG18/13 and RG33/12) and MOE Tier 2 (MOE2014-T22-015 ARC 4/15).

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Part I

Basics of Wireless Energy Harvesting and Transfer Technology

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1

Basics of Wireless Energy Harvesting and Transfer Dusit Niyato, Ekram Hossain, and Xiao Lu

1.1

Introduction Energy harvesting is an important aspect of green communication that provides self-sustainable operation of wireless communications systems and networks. Energy harvesting has been adopted in low-power communication devices and sensors. There are different forms of energy harvesting suitable for different applications. Table 1.1 shows the summary of different energy harvesting technologies. •

•

Photovoltaic technology has been developed over decades, and it is one of the most commonly used energy harvesting techniques. A solar panel which is composed of multiple solar cells converts sunlight into a flow of electrons based on the photovoltaic effect. The effect describes the phenomenon that the light excites electrons into a higher state of energy. The electrons then can act as charge carriers for electric current. A solar cell contains a photovoltaic material, e.g., monocrystalline silicon, polycrystalline silicon, amorphous silicon, and copper indium gallium selenide/sulfide. The efficiency of a solar cell can be up to 43.5%, while the average efficiency of a commercial solar cell is 12%–18%. Photovoltaic technology has been adopted in many applications, including rooftop and building integrated systems, power stations, rural electrification, and telecommunication. However, photovoltaic systems need a large area and cannot supply energy during the night. Moreover, their efficiency depends on the orientation of the solar panel, which can be complicated to optimize. Photovoltaic systems are suitable for static data communication units, e.g., a base station and access point, while their applicability to mobile units, e.g., user equipment, is limited. Thermal energy or heat can be converted to electricity using a thermoelectric generator based on the Seebeck effect or Thomson effect. The effect describes the conversion of temperature difference and electricity in thermoelectric devices. While thermoelectric devices are typically used for measuring temperature, recently they have been developed to serve as energy sources. The devices can produce 20–16 μW/cm2 with the human body as a heat source at room temperature. The benefit of thermoelectric devices is the capability of generating

Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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Dusit Niyato et al.

Table 1.1. Different wireless energy transfer techniques [1] Power density

Output voltage

Availability

Circuit weight

Solar [2]

100 mW/cm2

Daytime only

5–10 g

Thermal [3]

60 μW/cm2

0.5 V (single Si cell), 1.0 V (single a-Si cell) N/A

Anytime

10–20 g

Ambient RF Vibration [4] Push button (piezoelectric) [5]

Up to 1 μW/cm2 20 μW/cm3 50 μJ/N

3–4 V 10–25 V 100–10000 V

Anytime Activity dependent Activity dependent

2–3 g 2–10 g 1–2 g

•

energy as long as there is a temperature difference or a heat flow. Additionally, since they do not have any moving parts, they have high reliability. However, the devices are bulky and heavy. Also, they can supply only a small amount of energy, with typical efficiencies of approximately 5%–8%. Vibration can cause mechanical strains that can be converted into electricity through the piezoelectric effect. Piezoelectric devices can continuously generate electricity as long as there is some vibration, e.g., from noise and wind. Human movement can let the piezoelectric devices generate electricity intermittently, e.g., arm motion and shoe impacts. It is also possible to harvest energy from blood pressure that can be delivered to implantable or wearable sensors. The output power in such a case has a density of around 250 μW/cm3 . Although the harvesting circuit has a light weight, it needs a large area and the output energy can vary drastically. A push button energy generation circuit has light weight and its size is relatively small. However, the conversion efficiency can be low.

Wireless energy harvesting is different from other forms of energy harvesting, e.g., solar, wind, and vibration. Firstly, energy sources for wireless energy harvesting can support regular and controllable energy supply with high efficiency for near-field energy transfer and over distance for far-field energy harvesting. Secondly, if energy harvesting nodes are fixed, usually their wireless energy supply will be relatively predictable since the efficiency depends on the distance. However, since the efficiency depends on the distance, the energy supply among nodes at different locations can be non-uniform. Thus, the capability of each node can be different, which makes the network operation more challenging. Figure 1.1 shows a generic block diagram of a wireless sensor device. The device is typically composed of three major components. •

•

Energy sources. An energy harvester can harvest and generate electricity from energy sources. As shown in Table 1.1, different energy sources can be used for different applications depending on the amount of energy, size, weight, etc. Power supply unit. This is responsible for regulating incoming electricity and storing it in an energy storage device such as a battery and capacitor. The power

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Basics of Wireless Energy Harvesting and Transfer

Energy sources Solar

Power supply unit Converter/ transducer

Main power output

Microcontroller unit (MCU)

Thermal Regulator Vibration RF

5

Energy storage

Sensors Power management unit (PMU)

Transceiver

Sensor subsystem

Figure 1.1 A generic model of an energy harvesting sensor device [1].

•

1.2

management unit (PMU) is designed to transfer energy from the energy storage to the sensor subsystem. The PMU may decide to switch on or switch off the sensor subsystem, e.g., when there is enough and not enough energy, respectively. The sensor subsystem is controlled by the microcontroller unit (MCU). The MCU interfaces with the sensors. Depending on the application, for example, the sensors can be a motion detector or video camera for surveillance. The MCU packetizes and transfers the data collected from the sensors to the transceiver. The transceiver transmits a data packet to a receiver. Moreover, the transceiver also receives a packet, e.g., a control signal, to adjust the operations accordingly.

History of Wireless Energy Harvesting and Transfer Technology The history of wireless energy harvesting and transfer can be traced back to 1819. Hans Christian Oersted performed an experiment and observed that a compass needle can be made to deviate from magnetic north because of the change of current from a battery. He found that electric current can induce a magnetic field around the wire that the current flows through. Thus, he established the relationship between electricity and magnetism. This finding served as a basis for André-Marie Ampère to develop mathematical models to capture and explain the relationship between electricity and magnetism. Ampère found that two parallel wires can repel or attract each other depending on the directions of electric currents. He then proposed Ampère’s law, which states that the force between two wires with currents passing through them is proportional to the lengths of the wires and the amounts of the currents. The later major developments following on from Ampère include the Biot–Savart law, Gauss’s law for magnetism, and Faraday’s law. The Biot–Savart law models the magnetic field generated by an electric current. The law describes the relationship among magnitude, direction, length, and proximity of the electric current and the intensity of the magnetic field. Gauss’s law for magnetism is related to the zero divergence of a magnetic field. Faraday’s law describes the phenomenon that a change of magnetic flux can induce an electromotive force in a circuit. The amount of force is a function of the rate of change. James Clerk Maxwell established a set of partial differential equations, called Maxwell’s equations, that characterize the effect of electric and magnetic fields

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generated and varied by each other. They are related to the change of currents. In 1873, he published a book titled A Treatise on Electricity and Magnetism [6] that momentously lays down the fundamentals of electricity and magnetism. The aforementioned discoveries and theories established the modern theoretical foundation of electromagnetism that has found numerous applications in electronics, telecommunications, and electrical power engineering. In the context of wireless energy transfer, Heinrich Rudolf Hertz postulated the existence of electromagnetic waves. He experimented and demonstrated their existence by using an oscillator connected to induction coils. These coils radiated electric and magnetic fields as transverse waves. The detector designed as a ring was able to measure the magnitude and direction of the waves as well as their polarity and reflection. This was the first experiment to show that electricity can be transmitted through the air. The remarkable development of wireless energy transfer technology was achieved by Nikola Tesla, the founder of alternating current electricity. He was the first to experiment on wireless power transfer using microwave technology in the period 1891–1904. He demonstrated a system of inductive and capacitive coupling to transmit energy wirelessly. The system is based on spark-excited radio-frequency (RF) resonant transformers. The transformers are currently known as Tesla coils. The system is able to show the wireless energy transfer capability to illuminate light bulbs a short distance away. Later, he tried to increase the distance. The method used was based on resonance inductive coupling. However, the distance is still within 100 m. To increase the transmission range further, Tesla considered the RF energy transfer technique. He constructed the Wardenclyffe Tower, which is a large high-voltage coil infrastructure. The purpose was to demonstrate his vision of a “World Wireless System.” Although the construction was never finished, it can be considered as the first attempt to achieve long-range RF wireless energy transfer technology. In 1964, William C. Brown developed a rectenna to convert microwaves to electricity. Brown demonstrated the applications of such a concept by developing a model helicopter powered wirelessly. In 1975, Brown managed in an experiment to transfer 30 kW of power over a distance of 1 mile with 84% efficiency. A similar idea was adopted in a solar power satellite introduced in 1968. The idea is to place a large solar power satellite in geostationary Earth orbit. The satellite receives sunlight and converts it into electricity before transmitting the energy back to the Earth using microwaves. It is only recently that research and development in wireless charging have received tremendous momentum. With regard to applications to supply and recharge portable electronic devices, many manufacturers now see the commercial potential of the technology, e.g., [7]. In 2007, WiTricity technology was introduced. In experiments, this mid-range non-radiative wireless charging based on near-field resonant inductive coupling can supply energy to a 60 W light bulb. An efficiency of 45% and 90% is achieved at a distance of 7 and 3 feet, respectively. The experimental system is based on two five-turn copper coils with 60 cm diameter. An efficiency of 45% was achieved. The coils, arranged to be on the same axis, resonate at 9.9 MHz. The Cota system (www.ossiainc.com), PRIMOVE (primove.bombardier.com), and Powercast wireless rechargeable sensor system (www.powercastco.com) use similar technology. Powercast Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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is based on RF energy harvesting that can receive energy from a dedicated or ambient RF source. The devices are designed to support battery charging and capacitor charging in battery-free devices. The frequency of energy harvesting is 850–950 MHz, and it is able to work with 50  antennas. The output voltage is configured to be 4.2 V and 5.25 V. It is claimed that a conversion efficiency of 70% can be achieved. Combined with an advanced antenna system, magnetic MIMO was designed to support multi-antenna beamforming for magnetic waves of wireless energy transfer. The major standardization organizations for wireless energy transfer are the Wireless Power Consortium (www.wirelesspowerconsortium.com), Power Matters Alliance (www.powermatters.org), and Alliance for Wireless Power (www.rezence.com). Different producers adopt different standards; however, technology convergence is expected in the future.

1.3

Wireless Energy Harvesting and Transfer Technology Wireless technologies can be broadly classified into two major types, i.e., non-radiative coupling-based charging and radiative RF-based charging [8] as shown in Figure 1.2. The former is mostly used for near-field charging, while the latter is suitable for farfield charging. Non-radiative coupling-based charging can be divided into inductive coupling [9], magnetic resonance coupling [10], and capacitive coupling [11]. They are based on using magnetic flux to carry energy from a transmitter to a receiver. The attenuation of the magnetic field is a cube of the reciprocal of the distance. The absorption of the magnetic field affects the transmitter, e.g., the current. Alternatively, radiative RF-based charging can be classified into directive and non-directive RF power transfer [12]. They are based on using an RF signal and beam to transfer energy from a transmitter to receivers. The attenuation of the RF signal depends on the reciprocal of the distance, and the absorption of the RF signal does not impact the transmitter. Table 1.2 summarizes and compares different wireless energy transfer techniques [13].

Figure 1.2 Classification of wireless charging technologies.

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Table 1.2. Different wireless energy transfer techniques [13] Techniques

Effective distance

Efficiency

Applications

RF energy transfer (far field, radiative)

A few centimeters to hundreds of meters

Wireless sensor network [15], wireless body network [16]

Resonant inductive coupling (near-field, non-radiative) Magnetic resonance coupling (near-field, non-radiative)

A few millimeters to a few centimeters

0.4%, above 18.2%, and over 50% at −40 dBm, −20 dBm and −5 dBm input power, respectively [14] From 5.81% to 57.2% for frequency 16.2– 508 kHz [17] From 90% to 30% for distance 0.75– 2.25 m [10]

PHEV charging, phone charging

A few centimeters to a few meters

RFID tags, contactless smart cards, phone charging

Figure 1.3 Major components of a non-radiative wireless energy transfer system [8].

1.3.1

Non-Radiative Wireless Energy Transfer Figure 1.3 shows a general block diagram of a non-radiative wireless charging system [8]. The transmitter receives energy in a form of alternating current (AC) with a frequency of 50–60 Hz. However, this frequency is too low to be used for induction. Thus, the AC is converted to direct current (DC) using an AC/DC rectifier. The DC will be converted by the DC/DC converter to increase the voltage. The DC/AC inverter changes DC to AC with higher frequency and passes it to the transmit coil. The coil generates a magnetic field. At the receiver, which is separated from the transmitter by an air gap, the receive coil is induced by the magnetic field from the transmitter. The converts the AC to DC. The DC/DC converter adjusts the voltage to make it suitable for the load. In the following, we give an overview of two major non-radiative wireless energy transfer technologies, i.e., inductive coupling and magnetic resonance coupling.

1.3.1.1

Inductive Coupling Magnetic inductive coupling uses magnetic field induction as a means to transfer energy between two coils (Figure 1.4). A primary coil is used as a transmitter, while a secondary coil is used as a receiver. The primary coil, which is made of a conductive material such as copper, is connected with an AC power source. The current flow from the source generates an oscillating magnetic field. The field propagates to the secondary coil, which

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Figure 1.4 Inductive coupling.

Figure 1.5 Orientation of the secondary coil.

is called the conducting coil. For effective energy transfer, the distance between the two coils is usually less than a wavelength of the frequency used for inductive coupling, which is in the range of kHz. At the secondary coil, the varying magnetic field induces an electric current for the receiver. Then, the current can be used to supply the load or it can be stored in an energy storage device such as a capacitor or a battery. The effective charging distance for the inductive coupling is within 20 cm, i.e., typically less than the diameter of the coils). The orientation of the secondary coil has a significant impact on the energy reception. Figure 1.5 shows the orientations that result in maximum and minimal magnetic linkage and thus induction. In the first scenario, the primary and secondary coils are aligned in such a way that a large amount of magnetic field passes through the secondary coil. This will result in high energy transfer efficiency. By contrast, in the second scenario, the secondary coil is aligned such that minimal magnetic field passes through, leading to low energy transfer efficiency. In general, the magnetic inductive coupling is easy to implement, flexible to operate, of high efficiency (for short-distance energy transfer), and of low cost. Therefore, it is suitable for commercial products such as radio-frequency identification (RFID) tags and mobile phone chargers. Table 1.3 shows a summary of some existing hardware implementations of inductive coupling. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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Table 1.3. Comparison among hardware Implementations of inductive coupling References

Technique

Output

Maximum charging efficiency

Maximum charging distance

Frequency

[19] (2010) [20] (2012) [21] (2013) [22] (2013) [23] (2014)

0.18 μm CMOS 0.5 μm CMOS 0.18 μm CMOS 0.18 μm CMOS 0.13 μm CMOS

1.8 V 3.1 V 3V 1.5 V 3.6 V

54.9% 77% 87% 82% 65%

10 mm 80 mm 20 mm 11.35 mm 20 mm

13.56 MHz 13.56 MHz 13.56 MHz 100–150 kHz 40.68 MHz

Figure 1.6 Magnetic resonance coupling.

Inductive coupling systems can be designed based on one of the four basic topologies, i.e., series–series, series–parallel, parallel–series, and parallel–parallel [18]. The series– series and series–parallel topologies are more commonly adopted. In contrast, parallel– series and parallel–parallel topologies can yield better performance. However, they require sophisticated circuit design and performance tuning.

1.3.1.2

Magnetic Resonance Coupling Magnetic resonance coupling was developed to improve the energy transfer. It is based on evanescent wave coupling. As in inductive coupling, there are two coils, i.e., primary and secondary coils. However, the magnetic field is oscillating, and capacitances are added to the transmitter and receiver circuits (Figure 1.6). The oscillation is at the same frequency, typically in the MHz range, for the transmitter and receiver. Magnetic resonance coupling can achieve a higher efficiency and a longer charging distance than is possible with inductive coupling. Additionally, magnetic resonance coupling allows simultaneous charging of multiple devices which are tuned to the same frequency. Nonetheless, interference among coils can occur, meaning that optimal performance adjustment is required. With the setting of the magnetic resonance coupling system shown in Figure 1.6, the relationship among the transmitter current IS , the receiver current IL , and the mutual inductance M between the two circuits can be expressed as follows:   1 IL RL + jωLL + + zL = jωMIS , (1.1) jωCL

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where RL is the resistance of the receiver, LL is the inductance, CL is the capacitance, and zL is the complex impedance. ω is the resonance angular frequency of the system, which is obtained from 1 1 ω= √ =√ . (1.2) LS CS LL CL In coupling systems, not only is the receiver induced by the magnetic field from the transmitter, but also the transmitter is affected by the receiver. In this case, the voltage on the transmitter can be expressed as follows:   1 VS = IS jωLS + + zS + RT − jωMIL , (1.3) jωCS where IS is the current on the transmitter circuit, LS is the resistance of the transmitter, CS is the capacitance, and zS is the complex impedance. RT is the resistance of the transmitter. Notably, a magnetic resonance coupling system usually operates at the same resonance frequency. This can cancel the terms jωLL and 1/( jωCL ) for the receiver and the terms jωLS and 1/( jωCS ) for the transmitter. The receive power at the load of the receiver can be obtained from [24] PR = PT QT QR ηT ηR k2 (d),

(1.4)

where PT is the transmit power. ηT and ηR are the efficiencies of the transmitter and receiver, respectively. The efficiencies are obtained from zS zL , ηR = , (1.5) ηT = RT + zS RR + zL where QT and QR are the quality factors of the transmitter and receiver, respectively. RR is the resistance of the receiver. The quality factors are obtained from QT =

ωLS , RT + zS

QR =

ωLL . RR + zL

(1.6)

k2 (d) is the coupling coefficient between the transmit and receive coils as a function of distance d. It can be expressed as follows [25, 26]: k2 (d) =

rT3 rR3 π 2 (d2 + rT2 )3

,

(1.7)

where rT and rR are the radii of the transmit and receive coils, respectively. The resonance coupling system shown in Figure 1.6 is based on a single-input, singleoutput (SISO) configuration. It is possible to implement multiple coils at the transmitter and receiver, which are referred to as multiple-input, single-output (MISO) and singleinput, multiple-output (SIMO), respectively. Figure 1.7 shows a resonance coupling system with the MISO configuration with NT transmit coils. The receive power at the receiver from the transmit coil n can be obtained from [27] PnR = PnT QnT QR ηTn ηR kn2 (dn ), Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

(1.8)

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Figure 1.7 A multiple-input, single-output (MISO) magnetic coupling system.

Figure 1.8 A single-input; multiple-output (SIMO) magnetic coupling system.

where PnT is the transmit power of transmit coil n. QnT and QR are the quality factors of the transmit coil n and the receive coil, respectively. ηTn and ηR are the efficiencies of the transmit coil n and receive coil, respectively. dn is the distance between the transmit coil n and the receive coil. The coupling efficiency between the transmit coil n and the receive coil is similar to that in (1.7), i.e., kn2 (dn ) =

rn3 rR3 π 2 , (dn2 + rn2 )3

(1.9)

where rn is the radius of the transmit coil n. Thus, the total power at the receiver is given by PR = QR ηR

NT 

PnT QnT ηTn kn2 (dn ).

(1.10)

n=1

Figure 1.8 shows a resonant coupling system with the SIMO configuration with NR receive coils. As in the MISO configuration, the transmit coil is coupled with all the receive coils at the resonance frequency. Here, each receive coil generates and contributes to the total power of the receiver. The receive power at the receive coil m can be obtained from m m 2 Pm R = PT QT QR ηT ηR km (dm ),

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(1.11)

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Figure 1.9 A multiple-input; multiple-output (MIMO) magnetic coupling system.

where PT is the transmit power at the transmit coil, and QT and Qm R are the quality factors m of the transmit coil and receive coil m, respectively. ηT and ηR are the efficiencies of the transmit coil and receive coil m, respectively. dm is the distance between the transmit coil and the receive coil m. The coupling efficiency is expressed similarly to that in (1.9). Again, the total power at the receiver is PR = PT QT ηT

NR 

m 2 Qm R ηR km (dm ).

(1.12)

m=1

Figure 1.9 shows a resonance coupling system with the MIMO configuration with NT transmit coils and NR receive coils. This is a point-to-point MIMO transmission model in which the crosstalk between the transmit coils and receive coils is assumed to be small. The receive power at coil m from the transmit coil n is obtained from n n m n m 2 Pn,m R = PT QT QR ηT ηR kn,m (dn,m ),

(1.13)

2 (d where kn,m n,m ) is the coupling efficiency given the distance dn,m between transmit coil n and receive coil m. The coupling efficiency is obtained similarly to that in (1.9). Finally, the total receive power at the receiver is given by

PR =

NT  NR 

n m 2 PnT QnT Qm R ηT ηR kn,m (dn,m ).

(1.14)

n=1 m=1

Note that the details of the multiple-input, multiple-output configuration, i.e., MagMIMO, will be explained in Section 1.6.1. Table 1.4 shows a summary of hardware implementations of magnetic resonance coupling.

1.3.2

Radiative (RF) Wireless Energy Transfer Radio-frequency (RF), e.g., microwave, signals can be used as a medium to transfer energy. At the transmitter, alternating current is converted into a DC signal. The DC signal is transmitted as RF with a frequency typically in the range 300 MHz to 300 GHz.

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Table 1.4. Comparison among hardware implementations of magnetic coupling References

Transmit coil cross section

Receive coil cross section

Charging distance

Charging efficiency

Frequency

[10] (2007) [28] (2009) [29] (2012) [30] (2013) [31] (2014)

60 cm × 60 cm 21 cm × 21 cm 30 cm × 30 cm 35 cm × 30 cm 13.6 cm × 13.6 cm

30 cm × 30 cm 13 cm × 13 cm 30 cm × 30 cm 31.5 cm × 22.5 cm 5 cm × 5 cm

75 cm 1 cm 5 mm 20–31 cm 3 mm

93% 75.7% 74.08% 45%–57% 88.11%

9.9 MHz 134 kHz 15.1 MHz 144 kHz 22.2– 22.4 MHz

Figure 1.10 RF energy harvesting.

The RF signal propagates to the antenna of the receiver (Figure 1.10). The antenna can work on a single frequency or multiple frequencies at the same time, usually over a wideband frequency range. The propagation can be omni-directional or directional, i.e., beamforming. The omni-directional signal is used for energy broadcast applications but with low intensity. The directional signal, generated from an antenna array, is suitable for point-to-point energy transfer applications with high signal intensity. At the receiver, RF signal is rectified by a rectenna and converted into electricity. An impedance matching circuit is a resonator designed to operate at the specific frequency of the RF energy signal. The converted electricity is then fed to a voltage multiplier. In the voltage multiplier, a diode is used to convert AC signal into DC signal. A capacitor is connected to the voltage multiplier to regulate the DC current. The capacitor can also serve as a current reservoir if the DC signal temporarily drops or is not available. The efficiency of RF energy transfer depends on the efficiency of both transmitter and receiver antennas, the accuracy of the impedance matching to the frequency of energy transfer, and the efficiency of the voltage multiplier. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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Figure 1.11 Time switching and power splitting of the simultaneous wireless information and power transfer (SWIPT) technique.

Since data transmission and energy transfer are performed using RF signals, there are two approaches for information and energy transfer. •

•

Out-of-band RF energy transfer. In the out-of-band approach, the information and energy are transmitted using different frequencies. Thus, there is no interference between information and energy transmission. However, they require separate frequency bands. In-band RF energy transfer. The information and energy are transmitted over the same frequency. Information can be modulated with the RF energy signal.

For in-band RF energy transfer, the simultaneous wireless information and power transfer (SWIPT) technique was introduced [32]. SWIPT allows both information and energy transfer to be performed simultaneously using time-switching or power-splitting approaches (Figure 1.11). In the time-switching approach, the entire stream of RF signal is used for carrying either information or energy, and they are transmitted at different times. By contrast, in the power-splitting approach, the RF signal is divided into two streams, one of which is for the energy harvester and the other for the information receiver. The ratio of time switching and power splitting can be adjusted by incorporating various factors, e.g., channel quality and current residual energy. In RF energy transfer, the amount of energy that can be received by a receiver can be modeled as the Friis equation, as follows [33]: PR = PT

GT GR λ2 , (4πd)2 L

(1.15)

where PT is the transmit power of the transmitter, PR is the receive power of the receiver, L is the path-loss factor, GT and GR are the gains of the transmit and receive antennas, respectively, λ is the wavelength of the RF signal, and d is the distance between the transmit and receive antennas. The Friis equation is used for the free-space channel Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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model in which there is only a single path between a transmitter and a receiver. However, with different paths of signal, e.g., due to scattering and reflection, a two-ray ground model can be adopted for the case where there is a line-of-sight signal and a signal reflected from the ground before arriving at a receiver. The amount of energy at a receiver with a two-ray ground model is as follows: PR = PT

GT GR h2T h2R , d4 L

(1.16)

where h2T and h2R are the heights of the transmit and receive antennas from the ground, respectively. The free-space and two-ray ground models consider deterministic parameters of RF signal propagation. Alternatively, the randomness of signal propagation has to be captured in a model. Thus, a practical probabilistic model, i.e., the Rayleigh model, is widely adopted. The Rayleigh model considers propagation without a line-of-sight link between a transmitter and a receiver. For a Rayleigh fading channel, the amount of energy at a receiver is as follows: PR = PRdet 10L |r|2 ,

(1.17)

where PRdet is the received RF power obtained from a deterministic model. L is a pathloss factor, which is defined as L = −α log10 (d/d0 ), where d0 is a reference distance. r is a random number following a complex Gaussian distribution. RF energy sources can be classified into two major types, i.e., dedicated and ambient sources. •

•

Dedicated RF sources are similar to RF chargers that are deployed to supply energy for users and network nodes. Since they are designed for this specific purpose, the energy supply from dedicated RF sources is predictable and controllable. It is important to note that a regulatory authority, e.g., the Federal Communications Commission (FCC), can impose restrictions on RF sources since they can interfere with other wireless services. For example, for the 900 MHz band, the maximum transmit power is 4 W [34]. Ambient RF sources are RF transmitters which are designed for various purposes, not for energy transfer, for example, cellular base stations and TV towers. Although ambient RF sources are pervasive and their energy is free for wirelesspowered communication networks, they can supply only a limited amount of energy, e.g., because of long distances to receivers, and the energy supplied is random. Some ambient RF sources are static, e.g., TV towers, which always release a constant amount of energy, while others are dynamic in that the amount of RF energy released is variable, e.g., WiFi access points.

The amount of RF energy harvested is shown in Table 1.5. Different circuit designs have been proposed for RF energy harvesters. Table 1.6 shows a performance comparison among different circuit designs. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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Table 1.5. Experimental data for RF energy harvesting

1.4

Source

Source power

Frequency

Distance

Energy harvesting rate

Isotropic RF transmitter [35] Isotropic RF transmitter [36] Isotropic RF transmitter [37] TX91501 Powercaster transmitter [38] TX91501 Powercaster transmitter [38] KING-TV tower [39]

4W

902–928 MHz

15 m

5.5 μW

1.78 W

868 MHz

25 m

2.3 μW

1.78 W

868 MHz

27 m

2 μW

3W

915 MHZ

5m

189 μW

3W

915 MHz

11 m

1 μW

960 kW

674–680 MHz

4.1 km

60 μW

Wireless-Powered Communication Networks Wireless-powered communication networks can be construed as an extension of typical wireless networks with similar architectures. Figure 1.12(a) shows a centralized infrastructure-based architecture. As in a wireless network, there is an information gateway, e.g., a cellular base station or WiFi access point, serving mobile nodes. Additionally, there is an energy transmitter supplying wireless energy, e.g., inductive coupling, magnetic resonance coupling, or RF, to the mobile nodes. In this case, the mobile nodes have to be within the information transmission range in order to be able to communicate with the information gateway. Moreover, they have to be in the energy transfer range in order to be able to receive energy from the energy transmitter. The energy transfer range depends on the technologies used and can vary significantly. Figure 1.12(b) shows a decentralized infrastructure-less architecture. The communication among mobile nodes is direct peer-to-peer without connecting to a base station or an access point. The communication can be either single-hop or multi-hop communication. The concept of wireless-powered cellular networks was proposed in [64]. The networks have power beacons deployed to supply energy to mobile nodes or user equipment. The energy supply can be based on microwave radiation. This is called microwave power transfer. The user equipment harvests energy and stores it in energy storage devices (Figure 1.13). The transceiver utilizes the energy for information transmission and reception. The major challenges in developing wireless-powered cellular networks are as follows. •

•

To maximize the energy transfer efficiency, line-of-sight (LOS) links are required from the power beacons. With the LOS links, the network can achieve a close-tofree-space power transfer environment. Instead of letting the energy propagate in all directions, it is more efficient to beam the energy radiation at the power beacons to target user equipments. This reduces the adverse effect of propagation loss.

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Table 1.6. Performance comparison among different circuit designs Literature

Minimum RF input Peak conversion Frequency power at output voltage efficiency at RF input power

Technology

[40] (2006) [41] (2006) [42] (2007) [43] (2007) [35] (2008) [44] (2009) [45] (2009) [46] (2010) [47] (2011)

−19.58 dBm at 1 V Not applicable −17.7 dBm at 0.8 V −14.1 dBm at 1 V −22.6 dBm at 1 V −14.7 dBm at 1.5 V −25.5 dBm at 1 V Not applicable −24 dBm (4 μW) at 1V −32 dBm at 1 V Not applicable −17 dBm at 2 V −17 dBm at 2 V

[48] (2012) [49] (2012) [50] (2012) [51] (2012) [52] (2012) [53] (2012) [54] (2012) [55] (2012) [56] (2012) [57] (2013) [58] (2013) [36] (2013) [59] (2013) [60] (2013) [61] (2013) [62] (2013) [63] (2014) [37] (2014)

•

−22.5 dBm at 0.2 V −11 dBm at 1.08 V −3.2 dBm at 1 V −21 dBm at 1.45 V −21 dBm at 1.43 V 40 dBm at 30 V −10 dBm at 1 V 0 dBm at 1.2 V −16 dBm at 2 V −26.3 dBm at 1 V −39 dBm at 2.5 V −10 dBm at 2.2 V −20 dBm at 0.4 V −30 dBm at 1.9 V −15 dBm at 0.55 V −10 dBm at 1.3 V −27 dBm at 1 V

10.9% at −12 dBm 26.5% at −11 dBm 37% at −18.7 dBm Not applicable 30% at −8 dBm 15.76% at 12 dBm Not applicable 42.1% at −10 dBm 11% at −15 dBm

450 MHz 900 MHz 970 MHz 920 MHz 906 MHz 900 MHz 2.2 GHz 2.45 GHz 915 MHz

0.25 μm CMOS 0. 18 μm CMOS 0. 18 μm CMOS 0.18 μm CMOS 0.25 μ m CMOS 0.35 μm CMOS 130 nm CMOS SMS 7630 90 nm CMOS

Not applicable 22.7% at −3 dBm 60% at −3 dBm 60% 55% at −10 dBm Not applicable

915 MHz 2.4 GHz 868 MHz 868 MHz

130 nm CMOS 130 nm CMOS 0.130 μm CMOS 0.13 μm CMOS

900 MHz

HSMS-2852

83% at −1 dBm 65.2 % at −21 dBm 64 % at −21 dBm 85% at 40 dBm 10% at −10 dBm 70.4% at 0 dBm 58% at −3 dBm 31.5% at −15 dBm Not applicable Not applicable

2.45 GHz 900 MHz, 2.4 GHz 2.45 GHz 915 MHz 2.45 GHz 868 MHz 868 MHz AM band 900 MHz, 2.4 GHz 13.56 MHz 2.45 GHz 900 MHz 868 MHz

HSMS-2852 13 nm CMOS

55% at −30 dBm Not applicable 75% at −10 dBm 40% at −17 dBm

SMS-7630 SMS-2852 HSMS-2855 130 nm CMOS 90 nm CMOS Not applicable HSHS-2852 HSMS-286B HSMS-2850 HSMS-2852 90 nm CMOS

Owing to the limited energy supply from the power beacons, the energy consumption of the user equipment has to be minimized. This can be achieved, e.g., by using advanced energy management.

In this context, the authors of [64] pointed out the following issues. •

Power beacons can be designed, deployed, and operated with minimum cost. This is due to the fact that the power beacons do not require backhaul connections and powerful computation capability. Thus, a number of power beacons can be deployed densely to provide sufficient energy to user equipments.

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(a)

(b)

Figure 1.12 Centralized infrastructure-based wireless-powered communication networks.

Figure 1.13 A mobile node with a microwave power receiver.

• •

With multi-antenna systems and the availability of massive antenna arrays, power beacons have the ability to adjust energy beamforming for maximal performance. With the small-cell network concept, information transmission between user equipment and access points becomes local, thus reducing energy consumption significantly.

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The energy and information transfers can be performed on different frequency bands, avoiding severe interference. Alternatively, wireless-powered cellular networks can implement simultaneous wireless information-and-power transfer (SWIPT). SWIPT allows an item of user equipment to receive energy while transferring information simultaneously. For wireless-powered cellular networks, the authors of [64] also introduced a performance analysis model using tools from stochastic geometry. In this model, the access points are assumed to be distributed following a homogeneous Poisson point process (PPP). Items of user equipment are associated with the nearest access point. Each access point has a service area which is based on a Voronoi cell. The items of user equipment are randomly distributed in the service area, and the user equipment transmits data with a fixed power. Similarly, the power beacons are distributed [64] following a homogeneous PPP. In this setting, the analysis is able to derive the outage probability for user equipment, which is the probability that the user equipment is outside the network coverage.

1.5

International Standards Wireless charging and energy harvesting [1, 2] offers a quick and easy way to charge personal electronic devices without carrying around wired charging cords to plug into AC outlets for replenishment. With the quick development of hardware circuit design, wireless chargers are envisioned to be available in public areas, such as coffee shops and airport lounges, just like free Wi-Fi. Market analysis shows that more than 400 wireless charging products are available on retail sale. The increasing consumer applications have called for international standards to regulate the market. In this section, we introduce the standardization forums and the corresponding international wireless charging standards which have been released. We also overview the hardware implementation of these standards.

1.5.1

Standardization Forums The recent upsurge of interest in wireless charging research was driven primarily by the needs of the portable electronic device market. During the 1990s, commercialized wireless charging products began to emerge because of the explosive spread of portable electronic devices [7]. Both far-field- and near-field-based wireless charging approaches are undergoing rapid progress. For example, in 2007 Kurs et al. proposed the Witricity technology, shown in Figure 1.14(a). It was demonstrated through experiments that midrange non-radiative wireless charging is not only practical but also efficient. Moreover, low-power wireless charging has mainly found its applications in consumer electronics. For instance, wireless charging systems like the Cota system [4], PRIMOVE [69], and the Powercast wireless rechargeable sensor system [70] (illustrated in Figure 1.14(b)) have been commercialized. In addition, high-power wireless charging has been widely adopted in the field of transportation [71], such as in monorail systems [72] and for

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Figure 1.14 Illustrations of wireless power transmission systems: (a) the Witricity system, (b) Powercaster transmitter and harvester, (c) Qi charging pads, and (d) the magnetic MIMO system.

electric vehicles [73]. For example, Stanford University Global Climate and Energy Project has recently demonstrated that it is possible to deliver up to 10 kW of power over a distance of 6.5 feet, which can be used to simultaneously transfer power and charge moving vehicles [74]. The rapid development of wireless energy transfer techniques and their applications has called for standardization. Recently, different consortia, e.g., the Wireless Power Consortium (WPC) [72], Power Matters Alliance (Powermat) [73], and Alliance for Wireless Power (A4WP) [74], have been set up to develop and introduce international standards for wireless energy transfer technologies. Currently, some major standards have been adopted in many electronic products available in the market such as smartphones and wireless chargers. Some examples are shown in Figure 1.14(c).

1.5.1.1

Wireless Power Consortium The WPC was the first established open industry group, having been founded in November 2008. The WPC released its interface specification, namely Qi, in August 2009, and certified the first Qi-compliant product in September 2009. The first version of Qi [75] focuses on a tightly coupled inductive coupling technique across a range of power levels. Recently, the WPC has incorporated the implementation of magnetic resonance coupling into the Qi standard. Since its initial release, Qi has been undergoing rapid development. The WPC announced that by the end of 2014, more than 70 phones on the market had been built incorporating the Qi charging specification. And by the early of 2014, Qi was the only wireless charging technology available for vehicles [65]. By 2015, more than 200 companies had become members of the WPC. In addition, over 700 different electronic products have been certified to as being Qi-compliant [76].

1.5.1.2

Alliance for Wireless Power (A4WP) The Alliance for Wireless Power (A4WP) was formed in May 2012 and released its first specification in January 2013. The goal is to create an industry ecosystem that delivers wireless power transfer spatial freedom based on the application of magnetic resonance coupling. The A4WP technology features “spatial freedom,” which enables

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simultaneous charging of multiple devices with different power requirements from a single charger [77]. The key components of the A4WP framework concern the development of interoperability specifications, the establishment of a certification program, and participation in industry–government consultations regarding wireless power transfer [78]. The A4WP technology applies for loosely coupled wireless charging systems that are intended to meet next-generation user experience and industrial design requirements as part of the vision of ubiquitous power for portable, hand-held, consumer electronic devices.

1.5.1.3

Power Matters Alliance Powermat, founded in 2012, is another global, not-for-profit, industry organization aimed to provide wireless power for battery equipped devices using inductive-couplingbased charging technology [73]. Powermat has participated in IEEE Standards Association Industry Connections and proposed the original project authorization request to develop an IEEE-approved standard. With strong support from Powermat, the IEEE formed the IEEE Wireless Power and Charging Systems Working Group (WPCS-WG) in October 2013. At the beginning of 2015, Powermat and the A4WP officially teamed up to merge their technologies into a single standard, with the aim of establishing a core charging standard to support a wide range of consumer, medical, military and industrial applications.

1.5.2

International Regulations The wireless charging platform most widely adopted by the standardization forums is referred to as the “planar wireless charging surface” [79]. With the flat pad-like charging interface, one or more portable electronic devices can be put in place and charged simultaneously. In the design of planar wireless charging systems, the key design issues to be considered include safety, electromagnetic interference, and radiation exposure [80]. Specifically for radiation exposure, the following standards committees impose regulations on the planar wireless charging platform for wireless devices. •

•

The Comité International Spécial des Perturbations Radioélectriques (CISPR), also known as the International Special Committee on Radio Interference, is a special committee supported by the International Electrotechnical Commission (IEC). CISPR standards are oriented primarily toward electromagnetic emissions and measurements of electromagnetic emissions. The related requirements specified by CISPR 11 [81] on Industrial, Scientific, and Medical (ISM) Radio, CISPR 14 [82] on electromagnetic compatibility, and CISPR 22 [83] on information technology equipment should be taken into consideration. The European Standards Organizations (ESOs) consist of several European regional organizations, namely the European Committee for Standardization (CEN), European Telecommunications Standards Institute (ETSI), and European Committee for Electro-technical Standardization (CENELEC). Standards developed by any one of the ESOs are recognized as “European Standards.” The relevant specified requirements include EN55011 class B [84] on ISM radio,

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1.5.3

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EN55022 class B [85] on information technology equipment, and the EN62233:2008 [86] measurement method for electromagnetic fields with regard to human exposure. The FCC in the USA regulates interstate and international communications by radio, television, wire, satellite and cable. The related requirements specified by FCC part 15 class B [87] should be taken into consideration.

Current Standards This section introduces the basic charging methods of two international standards, namely Qi and A4WP. The Powermat standard is omitted because it is not publicly available. The ongoing standardization studies in communication communities are also reviewed.

1.5.3.1

Qi Qi (pronounced “chee”) is a wireless charging standard developed by the WPC [72]. It was first released in August 2010. Qi has been widely adopted in the electronics industry. Figure 1.15 shows a typical Qi-compliant system model. In particular, the Qi standard specifies interoperable wireless power transfer and data communication between a wireless charger and a charging device [88]. In the Qi standard, the charging device is controlled for charging procedures. The Qi-compliant charger is capable of adjusting the transmit power density as requested by the charging device through signaling. Qi adopts the magnetic inductive coupling technique. Thus, it supports wireless power transfer within a range of 40 millimeters. The Qi charger specifies two categories of power requirement. • •

Low-power category. The charging device can receive power up to 5 W in the 110–205 kHz frequency range. Medium-power category. The charging device can receive power up to 120 W in the 80–300 kHz frequency range.

In the first released specification, i.e., version 1.0, the Qi charger delivers 5 W of power into a power receiver. Version 1.1 of Qi offers a more flexible charger design with 12 different optional specifications. Moreover, the sensitivity of foreign object detection has been increased to prevent heating of metal objects surrounding active chargers. The current Version 1.2 further allows fast charging with up to 15 W power

Figure 1.15 The Qi-compliant wireless power transfer model. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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(a)

(b)

(c)

Coil Coil

Coil Coil Coil Charging Pad Guided Positioning (Magnetic Attraction)

Charging Pad Free Positioning (Moving Coil)

Charging Pad Free Positioning (Coil Array)

Figure 1.16 Models of a wireless charging system.

delivery and the corresponding receiver-side option to adapt to the high power. The WPC is continuing to increase design freedom for the Qi-compliant device developers. In the coming years, the Qi standard is expected to include more choices in power levels (from 5 W to 2000 W), transfer distances (between 0 and 5 cm), and charging area, as well as low-cost solutions [76]. In the standard design, a Qi wireless charger has a flat surface, called a charging pad. A charging device can be laid on top of the pad. As mentioned earlier, the tightness of coupling is an important factor determining the inductive charging efficiency. To achieve tight coupling, a charging device must be strictly placed in proper alignment with the charger. Qi specifies three different approaches for alignment [89]. •

•

Guided positioning. Shown in Figure 1.16(a) is a one-to-one fixed-positioning charging that provides guidance how a charging device should be placed. The aim is to achieve an accurate alignment. The Qi specification guides the charging device into a fixed location by using a magnetic attractor. To facilitate guided positioning, two methods can be applied. The first method is to adopt a standard socket or cradle [92] to locate the charging device in the best charging position. The second method is to guide the charging device to the best position by using a magnet and a magnetic attractor [93]. The advantage of this guided alignment approach is simplicity. However, it requires that a piece of material attracted by a magnet be deployed in the charging device, which can be complicated and costly to implement. Moreover, eddy-current-related power loss as well as the resultant high temperature will be induced in the magnetic attractor [90]. Free positioning with a movable primary coil. This is shown in Figure 1.16(b). It is also a one-to-one form of charging that is able to determine the location of the charging device. This approach needs a mechanically movable primary coil that tunes its position to bring about coupling with the charging device. This capability can be achieved by either inductive or capacitive means. For one charging device, the implementation of this alignment approach is simple and

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cost effective. However, the movable mechanical components tend to make the systems less reliable and less durable. Furthermore, for multiple charging devices, the motor control for the primary coils can be complicated and costly. Free positioning with a coil array. As shown in Figure 1.16(c), this allows one to charge multiple devices concurrently regardless of their positions. The Qi specification supports the “vertical-flux” approach [95] that uses an entire charger surface for power transfer without any restriction on the orientation of the secondary coil. For example, this free-positioning approach can be based on the three-layer coil array structure [96]. In comparison with the guided positioning and free-positioning approaches, this free-positioning approach is more userfriendly, but it incurs more cost, a complex winding structure and complicated control electronic element.

For data communication between the Qi charger and charging device, in-band communication is used. The data transmission and wireless power transfer are performed on the same frequency band. The Qi communication and control protocol has been developed to enable a Qi wireless charger to adjust its power output to meet the demand of the charging device. Moreover, it can be used to cease power transfer when charging is finished. The protocol works as follows. •

•

•

•

Start. The objective of this phase is to detect a potential objective for charging. During this phase, a Qi charger senses the presence of a potential power reviver. In Qi specification, object detection can be performed in two ways, namely the resonance shift method and the capacitance change method [97]. Ping. During this phase, the Qi charger begins to transmit the power signal. In the Qi standard, the power signal is the magnetic flux generated by the primary coil of a Qi charger which induces an electric current in the secondary coil of the power receiver. The power reviver first detects the actual amount and rate of wireless power harvested, which is dependent on the temporal transmission conditions. Then the receiver responds to the Qi charger by acknowledging the received signal strength, and the Qi charger detects the response. Identification and configuration. This phase is to determine whether the Qi charger can service the power receiver. In other words, this step identifies whether the power receiver and Qi charger are operating on the same set of power transfer protocols, or versions of a protocol. Specifically, the power receiver indicates its identifier and required power while the Qi charger configures energy transfer. During this phase, any violation in the contract terms could stop power transfer. Power transfer. The power receiver feeds back the control data, on which basis the Qi charger performs energy transfer. During this phase, the communication module keeps verifying the correctness and the order of received packets, as well as timing violations associated with various packets. The controller unit utilizes the information provided by the communication module to start, terminate, and re-configure the density of wireless power transmission.

Figure 1.17 presents a diagram of the control flow between a Qi charger and a power receiver in different phases. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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Qi Charger

(a)

Re-configuration requested

Start

Object detected

Ping

Power transfer requested

No response from receiver

Indentification and configuration

Power transfer contract established Power Transfer Timing violation/ power transfer contract violation

Timing violation

Phases of operation in Qi charger Power Receiver

(b)

Request re-configuration

Start

Power signal available

Ping

Power signal not available

Power signal available

Indentification and configuration

Power transfer contract established Power Transfer

Power signal not available

Power signal not available

Phases of operation in power receiver Figure 1.17 Reference models of near-field wireless power transfer protocol.

1.5.3.2

A4WP Owing to the limitations of the Qi standard, the A4WP designed a wireless power transfer technique that is able to support “spatial freedom” [78]. The A4WP standard is based on magnetic resonance coupling, which can generate a larger electromagnetic field. To achieve spatial freedom, the A4WP standard does not require a precise alignment. It can support some degree of separation between a charger and charging devices. In the standard, the maximum charging distance is up to a few meters. Moreover, the standard can support the charging of multiple devices with different power requirements simultaneously. For example, it can charge a Bluetooth headset with a power requirement of 1 W, a mobile phone (3.5 W), a smartphone (6.5 W), tablets and laptops (10–30 W) [78]. Moreover, A4WP overcomes the shortcoming of Qi in that A4WP allows foreign objects to be placed on an operating A4WP charger without causing any adverse effect. Therefore, it improves flexibility and convenience for users as the A4WP charger can be embedded in any object. The reference model of A4WP-compliant wireless power transfer standard is shown in Figure 1.18. The power transfer model consists of two components, i.e., power transmitter unit (PTU) and power receiving unit (PRU). The PTU transfer wireless power to the PRU. The transfer is controlled by a charging management protocol in the standard. In particular, feedback signaling is used between the PRU and PTU to help control and optimize the charging. The wireless power is generated and transferred at the frequency of 6.78 MHz , which is an Industrial Scientific Medical (ISM) band. Unlike Qi, A4WP

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Table 1.7. Specifications for power transmitter unit PTU

Power input

PRU support requirement

1 2 3 4 5

On roadmap 10 W 16 W 22 W On roadmap

PRU category 1 Multiple PRU category 1, 2, 3 concurrently or a single PRU category 4 On roadmap

Figure 1.18 A4WP-compliant wireless power transfer model.

uses out-of-band communication for control signaling. Data communication is done on the 2.4 GHz ISM band. •

•

A PTU or A4WP charger has three main functional units, i.e., resonator and matching circuit components, power conversion components, and signaling and control components. The PTU can be in one of the following function states: Configuration, PTU Power Save, PTU Low Power, PTU Power Transfer, Local Fault State, and PTU Latching Fault. In the Configuration state, the PTU performs a self-check. In the PTU Power Save state, the PTU periodically monitors and detects changes of impedance of the primary resonator. In the PTU Low Power state, the PTU sets up a data connection with PRU(s). The PTU Power Transfer state is for regulating power transfer. A Local Fault state happens when the PTU detects any local fault conditions such as overheating. PTU Latching Fault state happens when rogue objects are detected or when system errors or other failures are reported. The A4WP PRU is composed of the components for energy reception and conversion, control, and communication. The PRU has the following functional states: Null, PRU Boot, PRU On, PRU System Error, and PRU System Error. In Null state, the PRU is under voltage. In PRU Boot state, the PRU establishes a communication link with the PTU. In PRU On state, the communication is performed. PRU System Error happens when there is an over-voltage, over-current, or overtemperature alert. PRU System Error state happens when there is an error that has to shut down the power.

Tables 1.7 and 1.8 show the different classes of the PTU, e.g., for power input, and different categories of PRU, e.g., for power output. Note that no power exceeding that specified shall be drawn for both PTU and PRU. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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Table 1.8. Specifications for power receiving unit PRU

Power input

Application

1 2 3 4 5

On roadmap 3.5 W 6.5 W On roadmap

Low-power application (e.g., on order of 1 mW) Future phone Smartphone High-power applications (e.g., tablets and laptops)

Figure 1.19 Topology of an A4WP charging system.

The basic architecture of an A4WP wireless charging system is a star topology as shown in Figure 1.19. A single PTU, i.e., A4WP charger, is able to interact with one or more PRU(s), i.e., power receiver(s), for simultaneous power replenishment. Note that the power signal goes strictly from PTU to PRU(s). In addition, there is a functional and physical separation between the wireless charging and power control management [78]. Similarly to the Qi standard, A4WP also specifies a communication protocol to support wireless power transfer functionality. Bluetooth Low Energy (BLE) is adopted in A4WP-compliant systems for the control of power levels, identification of valid loads, and protection of non-compliant devices. The A4WP BLE profile provides the link for the following purposes. • • • •

The PTU resonator current is adjusted by the PRU. PRU-specific data can be conveyed to the PTU. PTU-specific data can be conveyed to the PRU. PTU can control PRU charge prioritization. The A4WP communication protocol has three steps.

•

Device detection. The PRU which needs to be charged sends out an advertisement message. The PTU which receives the message replies with a connection request. Upon receiving any connection request, the PRU stops sending the advertisement message and establishes a connection to the PRU.

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Information exchange. The PTU and the PRU exchange their Static Parameters and Dynamic Parameters as follows. – – – –

•

1.5.3.3

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The PTU receives and reads the information of the PRU Static Parameters. The parameters include its status and other system settings. The PTU sets its capabilities in the PTU Static Parameters and sends them to the PRU. The PTU reads the PRU Dynamic Parameters that include PRU current, voltage, temperature, and functional status. The PTU then specifies in the PRU Control how to manage the charging process.

Charging control. This is initiated by the PTU with PRU Control. The PTU must have enough power to meet the PRU’s demand. The PRU updates Dynamic Parameter periodically to inform the PTU of the latest information. The PTU can adjust PRU Control for charging accordingly. If a system error or complete charging event is detected, the PRU sends an alert notification message to the PTU. The PRU Dynamic Parameter includes the reason for the alert.

Other Ongoing Standardization Efforts Other than the WPC, PMA, and A4WP, a variety of organizations across the world are also actively making standardization efforts on wireless charging. The IEEE has formed the Wireless Power and Charging Systems Working Group, which designated IEEE P2100.1 standard specifications for wireless power and charging systems. It is expected that IEEE P2100.1 will be the first IEEE standards series that addresses parallel wireless power and charging technology specifications. The International Telecommunications Union (ITU) has also initiated wireless charging standardization research. The correspondent team, designated ITU-R WP1a, is attempting to address how the ITU should establish wireless power transmission standards. Moreover, the International Electrotechnical Commission (IEC) and the Consumer Electronics Association (CEA) are making efforts to develop specifications for consumer electronic products. In addition, another special interest group, namely the Society of Automotive Engineers (SAE), has been developing standards on wireless charging for electric and hybrid vehicles.

1.5.4

Hardware Implementation of Wireless Charging Standards With the popularity of wireless energy and power transfer technologies, prototype design and development become important research directions to determine an optimal system architecture and functional feasibility. In this regard, the Qi standard has mostly been adopted for experiment due to ease of implementation and it has been introduced before other standards. In the following, we review these hardware designs. In [98], the authors introduced implantable medical devices with wireless power transfer and a Qi-compliant charger. The charger uses a Bluetooth low-power communication module for remote control and supervision of the devices. The communication module also facilitates remote control of the device’s charging cycle, real-time

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batteries, and system status acquisition. With 3 W output power, the developed prototype was shown to achieve a maximum efficiency of 75%. Instead of using singledirectional charging, the authors in [99] performed a performance evaluation of bidirectional wireless charging between portable devices under the WPC Qi specifications. With an output power of 2.5 W, the prototype can achieve a charging efficiency of 70% at a distance of 2 mm, which is reasonable for most charging applications. The authors of [100] and [101] built their prototype with integrated circuits. The authors of [100] introduced a Qi-compliant wireless charging system including a wireless power transmitter and a wireless power receiver. The power transmitter adopts a full-bridge resonant inverter and a full-bridge variable voltage regulator as the architecture. The prototype systems were implemented using an integrated circuit and discrete components. The experimental results showed that 70% charging efficiency was achieved at 5 W output power for a 5 mm charging distance. In [101], the authors presented the design of a fully integrated Li-ion battery charger in accordance with the Qi standard. With a constant current, maximum and average charging efficiencies of 83% and 79% were achieved, respectively. Charging device position is an important issue when one wants to achieve high charging efficiency. Therefore, the authors of [97] and [90] studied the alignment control. They introduced the design of a control unit and communication controller for guided positioning of a single-receiver wireless charging platform. The control unit can determine the response time values. It also performs the data exchange between charger and receiver, and selects the operating frequency based on a serial communication interface. Then, the function of the communication controller is to initiate, monitor, and control wireless charging. Moreover, additional data processing and storage capability were proposed. The adaptive design is beneficial in terms of response time and the size of control data transfer. The experiment was conducted for the prototype, and it was shown that the hardware design complexity and internal power consumption of both power transmitter and receiver can be significantly reduced. To improve the device positioning accuracy, a design based on a single-layer winding array to enable multiple-device simultaneous charging in a free-positioning manner was introduced [90]. The authors use mathematical packing theory in the system and design to localize the charging flux within the covered charging area. This helps enable the free placement of the devices, i.e., secondary coils, improving the convenience of users substantially. Experiments showed that the power transfer efficiency is in the range of 86%–89% for any position of the charging device. In [91], the authors evaluated and compared four different power conversion methods for Qi-compliant wireless power transfer applications. They are voltage control, duty-cycle control, frequency control, and phase-shift control. The experimental results indicate that the phase-shift control method outperforms other methods considerably. However, the design and implementation of the circuit for the phase-shift control method is more complex and more expensive. The use of phase-shift control can improve the overall system efficiency to 72% for 5 W wireless charging. More recently, the authors of [103] demonstrated a family of wireless chargers that are able to work under a variety of operating modes. The corresponding multi-mode Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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Table 1.9. Comparison among different wireless charging systems System

Source power

Frequency

bf Effective charging distance

RAVpower [104] Duracell Powermat [105] Energizer Qi [106] Writicity WiT-2000M [107] UW prototype [108] Writicity WiT-3300 [109] MagMIMO [110]

7.5 W 18 W 22 W 12 W 30 W Up to 3.3 kW 20 W

110–205 kHz 235–275 kHz 110–205 kHz 6.78 MHz 13.56 MHz 85 kHz 1.0 MHz

8 mm 5 mm 11 mm 20 mm 100 mm 150 mm 400 mm

wireless PRU enables a portable electronic device to be charged with any one of three wireless power standards: Qi, Powermat, or A4WP. With an input voltage of 5 W at a PTU, the measured charging efficiencies at the PRU are all over 65% for any standard. In Table 1.9, we provide a comparison among the selected wireless power transfer and charging systems. The source power, frequency, and effective charging distance are considered.

1.6

Implementation Examples In this section, we describe the implementations of MagMIMO and Powercast for nonradiative and radiative (RF) energy transfer systems.

1.6.1

MagMIMO MagMIMO was introduced to address many limitations of near-field energy transfer techniques [110]. While the concept is similar to MIMO used in a communication system that is based on RF radiated field, MagMIMO transfers energy using non-radiated magnetic field beamformed directly toward a receiver, e.g., a mobile phone. In MagMIMO, an energy transmitter has multiple transmit coils and a receiver has a single receive coil. The currents applied to different transmit coils are optimized jointly so that the receive coil can constructively combine the magnetic fields. This not only improves the efficiency, but also supports position variability of the receive coil. The MagMIMO prototype was built and tested with a commercial mobile phone. The major capabilities of the MagMIMO are as follows. •

•

•

MagMIMO can charge a mobile phone at a distance of 40 cm with satisfactory performance. This distance is much larger than that of current commercial wireless chargers, which work only at 1–10 cm. The charging efficiency of MagMIMO is much higher than that of other technologies. This results in a significantly shorter charging time. For example, MagMIMO has a charging time for a mobile phone only twice that of wire charging. MagMIMO can charge a mobile phone in any orientation, from perfect alignment at 0◦ to an orthogonal alignment at 90◦ . This is much more flexible than

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Figure 1.20 MagMIMO in a comparison with information transfer.

•

other wireless chargers that require perfect orientation of a mobile phone, e.g., within 30◦ . MagMIMO can charge a mobile phone from different places, e.g., in a pocket, on a desk, in a backpack. Nonetheless, the efficiency varies depending on the environment.

Figure 1.20 shows the structure of MagMIMO in comparison with information transmission MIMO. The fundamental concept of MagMIMO is the multi-coil magnetic beamforming, which is capable of optimizing magnetic flux along a beam. Such optimization allows the beam carrying energy to reach a distant receiver. To handle arbitrary orientation of the receiver, the magnetic flux can be adjusted in a certain direction. From Figure 1.20, there are two transmit coils at the MagMIMO transmitter. The coils generate and beam the magnetic field. The receiver, basically a receive coil, intercepts the magnetic field and converts it to electricity. To achieve the highest energy reception efficiency, the induced current at the receive coil, denoted by IL , must be maximized. This depends on the mutual inductances between transmit and receive coils, e.g., M1 and M2 as shown in Figure 1.20 for transmit coils 1 and 2, respectively. Extended from (1.3), the relationship between the induced current IL and source current IS is expressed as follows [110]:   1 (1.18) = jω(M1 + M2 )IS , IL RL + zL + jωLL + jωCL where RL , zL , LL , and CL are the resistance, impedance, inductance, and capacitance of the receiver, respectively. ω is the AC frequency at the transmitter. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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To maximize the induced current, the MagMIMO protocol was proposed in order to estimate magnetic channels from the transmitter to the receiver. Depending on the channel, beamforming is performed to optimize mutual inductances. These steps have to be performed iteratively because the orientation and distance away from the receiver can change. From (1.18), the induced current depends on the magnetic inductances. Thus, the “channel” is defined as follows [110]: mi =

jω Mi . zL + RL

(1.19)

With the channel, the induced current can be optimized by varying the source current IS . Thus, the magnetic beamforming is expressed as follows [110]: m∗i , 2 i=1 |mi |

βi = n

(1.20)

where m∗i is the complex conjugate of magnetic channel mi . The source current flowing through transmit coil i is βi IS . To estimate the channel, the transmitter measures the load on its coil as follows:   1 T T T T + zi − jωMi IL , (1.21) Vi = Ii jωLi + jωCiT where ViT is the voltage of the coil of transmitter i, IiT is the current, LiT is the inductance, CiT is the capacitance, zTi is the impedance, and Mi is the mutual inductance. Basically, the transmitter applies voltage ViT and measures the current IiT , while the coils of other transmitters are kept open circuit. The impedance can then be calculated from zi =

ViT IiT

= zTi − jωMi

IL . IiT

Finally, the magnetic channel is obtained from [110]  zi − zTi m ˜ i = j1sgn(Mi ) , RL + zL

(1.22)

(1.23)

where 1sign(Mi ) returns +1 if the sign of Mi is positive, and −1 otherwise. With the estimated magnetic channel m ˜ i , the transmitter adjusts the current in each coil such that ˜ i. IiT = βi IS , where βi utilizes the estimated channel m Figure 1.21 shows the efficiency of MagMIMO obtained in tests at varying distances.

1.6.2

Powercast Powercast is one of the popular RF energy transfer products (http://www.powercastco .com). The Powercast receiver, called Powerharvester, is able to harvest RF energy in a range of microwatts to milliwatts to supply low-power devices such as sensors and RFID. Thus, it can reduce or eliminate battery charging and replacement. The transmit power of the transmitter, called Powercaster, is bounded at 4 W, for which the RF-toDC conversion efficiency can be up to 70% depending on the scenario. Nonetheless,

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90 80

Efficiency (%)

70 60 50 40 30 20 10

0

5 10 15 20 25 30 35 Distance between transmitter and receiver

40

Figure 1.21 Efficiency of MagMIMO [110].

(a)

(b)

Figure 1.22 Powercast (a) kit and (b) receiver (http://www.powercastco.com/products/ development-kits/).

the Powerharvester can also work with other ambient or dedicated RF sources. The center frequency is 915 MHz, and can be tuned to work with the frequency range 850– 950 MHz. Nonetheless, some models can support a specific frequency, e.g., GSM-850 uplink, Europe RFID and GSM-850 downlink, ISM USA and GSM-900 uplink, GSM1800 uplink, GSM-1900 uplink, and Wi-Fi 2.4 GHz bands. The Powerharvester can work with a standard 50  antenna and can connect with a rechargeable battery such as alkaline, lithium ion, and Ni-HM batteries. The Powercast kit, i.e., P2110 model, is composed of the following major components (Figure 1.22(a)). •

A 3 W, 915 MHz Powercaster transmitter. It is able to transmit both energy and data, and has a built-in 8 dBi antenna. It has been certified by the FCC. The energy modulation is based on DSSS and the data modulation is based on amplitude shift keying (ASK). The transmitter can provide powers of around 160 and 40 μW at distances of 5 and 10 m, respectively.

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•

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Receiving antenna and Powerharvester evaluation board. They are able to receive both data and energy, and perform RF-to-DC conversion. The RF energy harvesting can be performed down to −12 dBm input. The evaluation board can be interfaced with a microcontroller unit (MCU), and during a development phase it connects with the application development platform to program the functions. With a 6 dBi receiver antenna, the available power before conversion is around 375, 100, and 25 μW at distances of 0.5, 1.0, and 2.0 m, respectively. Battery charging interface board. It can charge a local battery and also support rechargeable AA and AAA batteries. The regulated output voltage is 2.0 or 2.7 V and the under-voltage cut-off threshold is 2.1 V. It is connected to the Powerharvester evaluation board.

Powercast is used in unmanned vehicle charging [111, 112]. In [112], an unmanned vehicle provides RF energy for wireless sensor networks. The vehicle visits sensors periodically. It can select the sensors and determine a sojourn time to recharge them dynamically. The testbed based on evaluation board P2110-EVB of Powercast is used. Some modifications were introduced by the authors to meet the charging voltage of the sensors. Basically, the Powerharvester converts RF signal to DC and stores it in an external energy storage device, i.e., a storage capacitor or a battery. When the energy transmitter is transmitting RF energy, the Powerharvester charges the storage capacitor. If the DC voltage is higher than the threshold of the storage capacitor, the Powerharvester will stop charging the capacitor and start supplying energy output to the sensor board. The capacity of the capacitor will determine the amount of charging energy and charging time as well as the amount of energy supplied and the duration of energy supply, namely when there is and when there is not incoming energy from the transmitter, respectively. Note here that there is a leakage current of the capacitor. Thus, to maximize the amount of energy supplied and duration of energy supply to the sensor, the authors adopt a supercapacitor, i.e., an electrochemical capacitor or double-layer capacitor. It is an alternative to the electronic or dielectric capacitor, e.g., a ceramic and tantalum capacitor, and the battery. The supercapacitor has a higher energy density than that of a traditional capacitor. Compared with a rechargeable battery, the supercapacitor offers lower a charging voltage and a faster charging speed. Additionally, the supercapacitor supports many more charge and discharge cycles than a battery can. In the testbed, the authors use a 5 F Powerstor supercapacitor with 13 m internal resistance, and 25 μA leakage current with a surge voltage of 5.5 V. The Powerharvester is set to receive RF energy when the energy transmitter is at a distance of 18 cm. Note, however, that, to avoid an RF radiation overexposure effect, the transmitter has to stop sending RF energy if its distance from the Powerharvester is less than 18 cm. When the supercapacitor is fully charged, the transmitter will stop transmitting RF energy. Then, the supercapacitor releases energy output to the sensor. The sensor can operate, e.g., to send data to an access point, as long as the voltage supplied is above 2.45 V. The vehicle is programmed to return to the sensor before the supercapacitor depletes its energy. Figure 1.23 shows the approximated voltage of the storage capacitor for different sleeping periods and charging times of the sensor. When the sensor spends more time sleeping, it consumes less energy from the storage capacitor, and thus the voltage is Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 13 Jan 2017 at 07:21:36, .002

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Voltage of storage capacitor

3.5 3 2.5 2 1.5 Sleep for 65 seconds Sleep for 131 seconds Sleep for 262 seconds

1 0.5

0

50

100

150 200 250 300 350 Charging time (seconds)

400

450

Figure 1.23 Approximated voltage of a storage capacitor for different sleeping periods [112].

higher. Clearly, when the charging time increases, the voltage increases. When the voltage reaches the threshold, the Powerharvester will supply energy to the sensor to sense and transmit a packet.

1.7

Summary We have provided an overview of wireless energy harvesting and transfer technology. Firstly, we have discussed different types of energy harvesting and highlighted that wireless energy transfer is one of the most useful techniques. Then, a brief introduction to wireless energy harvesting and transfer has been provided. Three major techniques for wireless energy transfer, namely inductive coupling, magnetic resonance coupling, and RF wireless energy transfer, have been introduced. To discuss the feasibility of RF wireless energy transfer, experimental data based on the existing RF wireless energy transfer technologies have been discussed. The architecture of a wireless-powered communication network has also been introduced. We have also discussed the standardization activities on wireless energy harvesting and transfer along with some experimental results based on the existing standards.

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[108] A. P. Sample, B. H. Waters, S. T. Wisdom, and J. R. Smith. “Enabling seamless wireless power delivery in dynamic environments,” Proceedings of the IEEE, vol. 101, no. 6, pp. 1343–1358, June 2013. [109] Witricity Corp. Developers Kit for Mobile, data sheet “WiT-3300,” 2013 (available at www.witricity.com/assets/WiT-3300_R2.3_DS.pdf). [110] J. Jadidian and D. Katabi, “Magnetic MIMO: How to charge your phone in your pocket,” in Proc. Annual International Conference on Mobile Computing and Networking (MobiCom ’14), September 2014. [111] H. Dai, Y. Liu, G. Chen, X. Wu, and T. He, “Safe charging for wireless power transfer,” in Proc. INFOCOM, April–May 2014, pp.1105–1113. [112] F. Sangare, A. Arab, M. Pan et al., “RF energy harvesting for WSNs via dynamic control of unmanned vehicle charging,” in Proc. IEEE Wireless Communications and Networking Conference (WCNC), March 2015, pp. 1291–1296.

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Circuit Design for Wireless Energy Harvesting Min Jae Kim, Kae Won Choi, Dong In Kim, Youngoo Yang, Kang Yoon Lee, and Keum Cheol Hwang

2.1

Introduction To date, there have been a number of research proposals to explore the newly emerging wireless charging technologies based on radio-frequency (RF) signals, ambient or dedicated. In particular, research efforts towards achieving the goal of transmitting information and energy at the same time have been rapidly expanding, but the feasibility of this goal has not been fully addressed. Moreover, the respective coverage areas of transmitting information and energy are wildly different, the latter being considerably smaller than the former. This is because the receiver sensitivities are very different, namely −60 dBm for an information receiver and −10 dBm for an energy receiver [1, 2]. Owing to this limitation, recently a commercial implementation of RF energy transfer has been restricted to lower-power sensor nodes with dedicated RF energy transmitters, such as the Powercast wireless rechargeable sensor system [3] and the Cota system [4]. In this chapter, we discuss the implementation of long- and short-range RF energy harvesting systems, where the former is to provide far-field-based RF energy transfer over long distances with a 4 × 4 phased antenna array and the latter to provide biosensors with RF energy over short distances. An overall circuit design for these RF energy harvesting systems is described in detail, along with the measurement results to validate the feasibility of far-field-based RF energy transfer. We illustrate the designed test-beds which will be applied to develop sophisticated energy beamforming algorithms to increase the transmission range. Finally, a new research framework is developed through the cross-layer design of the RF energy harvesting system, which is intended to power a low-power sensor node, like the Internet-of-Things (IoT) sensor node. To this end, we present a circuit-layer stored energy evolution model based on the measurements which will be used in designing the upper-layer energy management algorithm for efficient control of the stored energy at the sensor node. The new framework will be useful because the existing works on RF energy harvesting do not explicitly take into account a realistic temporal evolution model of the stored energy in the energy storage device, like such as a supercapacitor.

Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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Test-Beds for Long- and Short-Range RF Energy Harvesting Systems In this section, test-beds to develop and evaluate the hardware and software for RF energy harvesting systems will be introduced. Using the test-beds, it will be possible to develop and evaluate optimized RF energy harvesting systems and algorithms for simultaneous wireless energy transfer and communication. This section also includes structures and features of the test-beds which are used for evaluating the performance of the RF energy harvesting systems. The RF energy harvesting test-beds consist of two modules. The first one is for high-power/long-range applications. It utilizes the 2.4 GHz band both for energy harvesting and for data communication. The second one is for low-power/short-range applications. It utilizes the 915 MHz band for RF energy harvesting and the 2.4 GHz band for data communication. Using the high-power/long-range test-bed module, we can verify how well the scheduling algorithm for simultaneous wireless energy transfer and communication works in realistic wireless communication environments. Using the low-power/short-range testbed module, we can realize and effectively verify the data gathering modules using various ultra-low-power sensors including bio-sensors.

2.2.1

Basics of RF Energy Harvesting

2.2.1.1

Friis Equation We need to approximately calculate the received signal power for the energy harvesting block of our test-bed. Although there are many factors that have an effect on the RF energy harvesting systems, the most critical are the distance and frequency between the RF power beacon (source or RF signal transmitter) and the energy harvesting device. The receivable power from the radiated RF signal from the beacon decreases fast as the distance increases. At the frequency range (usually under 8 GHz) of commercial wireless systems, the received signal strength is not much dependent on the environmental conditions. Therefore, crucial parameters for RF energy harvesting are the loss of energy due to distance, minimum harvesting signal level, and the transmit signal power. For commercial base transceiver systems, the transmit signal power is not adjustable according to the status of any special user equipment. Hence, the variables we can use in the system design are limited to wireless signal attenuation according to the distance and minimum harvestable signal level at the user devices [2]. We can calculate the spatial loss using the Friis equation as LossdB = −Gt − Gr − 20 log10 (c/f ) + 20 log10 (4πR),

(2.1)

where Gt is the transmitter antenna gain, Gr is the receiver antenna gain, c is the speed of light (3 × 108 m/s in air), f is the signal frequency, and R is the radius (distance between the transmitter and the receiver). From (2.1), the signal loss in air is proportional to the square of the distance between the transmitter and the receiver. As the frequency increases, the loss at the same physical distance is proportional to the square of the frequency. 10 Mar 2017 at 07:57:49, .003

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Figure 2.1 Calculated signal loss according to distance using the Friis equation.

Numerical example The loss at a distance of 1 m and a frequency of 915 MHz and with no transmit and receive antenna gains is calculated to be about 32 dB as follows: LossdB = −Gt − Gr − 20 log10 (c/f ) + 20 log10 (4π R)   3 × 108 + 20 log10 (4π ) = −0 − 0 − 20 log10 915 × 106 = −0 − 0 + 9.69 + 21.98 = 31.67 dB. Figure 2.1 shows the calculated signal loss according to the distance between the transmitter and the receiver using the Friis equation. Here, we assume that the frequency band is 2.4 GHz, the antenna gain of the receiver is 3 dBi, the antenna gain of the transmitter is 5 dBi, and the output power of the transmitter is 48 dBm. The path loss is calculated for distances from 0 to 10 m. The calculated results show that the received signal becomes about 0 dBm when the distance is 6 m, and a loss of 52 dB is obtained for a distance of 10 m with a received signal power of −4 dBm. Since we can see a drastic decrease of the received power with the increased distance, this calculation and calculated results are essential a-priori considerations for the system budgeting for the test-beds.

2.2.1.2

Features of the Energy Harvesting Circuit A wireless energy harvesting system should be designed to be as simple as possible using highly efficient circuit blocks [5]. The receivable RF signals are very small (usually under −10 dBm), and the system must continuously supply a large amount of current to the data communication block. High efficiency and low current consumption in the energy harvesting block are very important features which must be considered in the circuit design. In general, a wireless energy harvesting system consists of two main blocks. Right after the antenna, we have an RF-to-DC conversion circuit on which the efficiency and 10 Mar 2017 at 07:57:49, .003

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Figure 2.2 Block diagram of the RF energy harvesting system.

the minimum harvestable signal level rely. After that, there is an energy storage unit with a DC–DC converter. A battery or a supercapacitor is usually adopted for this block. The system block diagram is shown in Figure 2.2. A matching circuit is necessary for the RF region in order to improve the minimum harvestable signal level. The RF-to-DC conversion circuit is generally implemented using a Schottky diode to rectify the received signal. Therefore, the input impedance of the RF-to-DC conversion block is very low, and the matching network must transform the impedance to about 50  in order for the antenna to have almost no signal reflection [6]. The Li-ion battery or a supercapacitor is used for the storage unit. The regulated DC voltage is lower than the DC voltage required to charge the storage unit. Therefore, a highly efficient DC–DC converter is required in order to convert the regulated DC voltage to a high enough voltage level to charge the Li-ion battery or the supercapacitor. The energy harvesting system must be designed with a power consumption as low as possible and an RF-to-DC conversion efficiency as high as possible.

2.2.1.3

Overall System Configuration The test-beds include digital interfaces and provide flexible test conditions in order to develop and optimize the hardware and software for real wireless communication environments. In particular, a duty-cycle control is required for energy harvesting and data communication for the energy harvesting system using a single frequency band both for energy harvesting and for data communication. From this point of view, the test-beds utilize the 2.4 GHz Bluetooth low-energy (BLE) band for various further applications. The overall test-bed consists of three separate circuit blocks and two evaluation modules, as shown in Figure 2.3. The three circuit blocks are (A) a 2.4 GHz wireless power transmitter for high-power/long-range RF energy harvesting, (B) a long-range RF energy harvesting circuit and a signal source for short-range energy harvesting, and (C) a bio-sensor including a short-range RF energy harvesting circuit. The high-power/longrange test-bed module uses the 2.4 GHz band both for energy harvesting and for data communication, while the low-power/short-range test-bed module uses the 915 MHz 10 Mar 2017 at 07:57:49, .003

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Figure 2.3 Test-bed configuration for RF energy harvesting systems.

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band for energy harvesting and the 2.4 GHz band for data communication. The transmit power can be digitally adjusted using a USB interface both for the long-range and for the short-range energy harvesting test-beds. Each block can be individually evaluated. The RF energy harvesting test-beds developed have adjustability for various situations or environments, such as energy harvesting efficiency tests at various distances, communication algorithm optimization and development, testing various modulation schemes (OOK, FSK, etc.), simultaneous operation of energy harvesting and communication, and so on. To evaluate various RF energy harvesting modules or circuits, the two modules for high-power/long-range and low-power/short-range harvesting are developed. Each module has its own transmitter and receiver which can be individually evaluated and optimized. Each transmitter and receiver block can easily be replaced by other circuit blocks for evaluation and development. For the long-range RF energy harvesting test-bed, the 2.4 GHz band is adopted both for energy harvesting and for data communication by using the BLE with high energy efficiency. For the short-range RF energy harvesting test-bed, which is for systems using different frequencies for energy harvesting and communication, the industrial, scientific, and medical (ISM) band at 915 MHz is used for energy harvesting and another ISM band at 2.4 GHz is used for data communication. This short-range module can be used as a bio-sensor that can regularly monitor bio-electrical signals from the human body for IoT and/or bio-medical applications.

2.2.2

High-Power/Long-Range RF Energy Harvesting Test Module

2.2.2.1

System Configuration The overall system of the high-power/long-range RF energy harvesting test-bed is displayed in Figure 2.4. The high-power test-bed is designed for data communication and energy harvesting at 2.4 GHz. The 2.4 GHz BLE standard is adopted for data communication and a continuous wave (CW) single-tone signal is used for a power transfer system. The transmitter stage consists of the RF signal source at 2.4 GHz, a drive amplifier, a 1-to-16 way power splitter, a power amplifier, and a pattern antenna. The minimum input power of the power amplifier should be 0 dBm to measure characteristics of the long-range RF energy harvesting. The driver amplifier circuit is designed to amplify output power to 28 dBm and the 1-to-16 way power splitter is realized in such a way as to have the minimum output power of 2 dBm. In order to avoid restriction of measurement by the physical distance between the transmitter and the receiver, the output power of the power amplifier is changed by the external control. Therefore, the drive amplifier circuit is employed with the range of gain variable from −15 dBm to 23 dBm. The receiver stage includes the receiver antenna, matching network, RF-to-DC power converter, battery charger controller, and Li-ion battery. The RF-to-DC power converter mainly consists of Schottky diodes, which have very low input impedance. Without the matching network, most of the received signals would be reflected back, considerably decreasing the amount of energy harvested. In addition, a complex matching circuit has its own losses and also results in deterioration of bandwidth characteristics. Therefore, 10 Mar 2017 at 07:57:49, .003

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Drive Amplifier (Enable to change output power)

Power Amplifier Module

RF Output Signal Test Port

RF Sinal

Power Amplifier (16 elements)

4 × 4 Phased Array Antenna (2.4 GHz ISM band)

2.4 GHz Energy Transfer

Matching Circuit

RF/DC Converter

Receiving Antenna Input Test Port

Receiving Antenna (2.4 GHz ISM band)

Battery Charger (Supercapacitor)

Li-Ion Battery

External Power Supply

50

DC/DC Converter

Display

Figure 2.4 Block diagram of the high-power/long-range RF energy harvesting test-bed.

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Drive Amplifier 28 dBm Output

5–10 m 34 dBm Power Amplifier with pattern Antenna 4 × 4 Array

Figure 2.5 The designed high-power/long-range RF energy harvesting test-bed.

it is worth noting that a simple LC matching network is required in order to reduce the losses of the signals supplied to the RF-to-DC converter. Because the energy harvested by the RF-to-DC converter is accumulated in the energy storage unit, the battery charger is utilized to store the energy in the storage unit effectively. A supercapacitor as well as an Li-ion battery is employed to fulfill the system requirements. For some specific systems, the harvested energy is used directly instead of storing it in the storage unit. Although the output of the RF-to-DC converter is connected to the battery charger as usual, it is connected directly to the DC–DC converter during communication in order to provide power to the communication system without storage. As shown in Figure 2.4, the power amplifier modules are arranged in a 4 × 4 array to obtain a more directional radiation pattern. The radiation characteristics of the transmitted radio signal should be directional to compensate for the signal losses in the air. It is possible to measure the efficiency of the long-range RF energy harvesting test module over a sufficiently wide distance range. In addition, each power amplifier can be controlled separately, thereby measuring energy harvesting features at different distances. The designed long-range RF energy harvesting test module is illustrated in Figure 2.5. Not only are both transmitter and receiver modules available for individual test and performance verification, but also each module can be improved and investigated separately.

2.2.2.2

Design The design target for the long-range RF energy harvesting module is determined by using the Friis equation. Assume that the maximum distance between the transmitter and the receiver for testing long-range RF energy harvesting is 10 m and the available minimum RF signal in the energy harvesting unit is 0 dBm. According to (2.1), the loss is about 60.2 dB, and 60 dBm power must be transferred over a distance of 10 m. Because 60 dBm is a high output power level, it is impossible to realize a suitable RF 10 Mar 2017 at 07:57:49, .003

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Table 2.1. Summary of the design target determined by the Friis equation Parameter

Unit

Target

Frequency Output Power Target Distance Receiver Antenna Gain Transmitter Antenna Gain Minimum Required Power

GHz dBm m dBi dBi dBm

2.45 48 6–10 3 9 0

Note At the PA output

At the receiver input

power amplifier which can amplify up to such a level. The available maximum output power of the power amplifier is 48 dBm, 12 dB lower than the computed loss of 60.2 dB. The difference in gain levels can be compensated by using the transmitter and receiver antennas. For the given specifications such as the power, frequency, and distance, the calculated target parameters are obtained by using the Friis equation as listed in Table 2.1. The RF transmitter power, receiver gain, and transmitter gain are determined as 48 dBm, 3 dBi, and 9 dBi, respectively, at 2.45 GHz. The gain of 12 dB obtained by the transmitter and receiver antennas compensates for the signal losses at the distance of 10 m. As a result, the loss between the transmitter and the receiver is 48.2 dB, and such a level enables one to realize the long-range RF energy harvesting test system. Figure 2.6 shows the block diagram of the energy harvesting unit with the computed design target of each circuit. The power amplifiers are arranged in 16 elements, such that each element has power 34 dBm, to satisfy a total power of 46 dBm for the longrange RF energy harvesting test. The power amplifier circuit is designed by utilizing AVAGO MGA-43024, which is a three-stage high-power amplifier used at 2.4 GHz. When a single power supply of 5 V is applied to each internal bias circuit, the 1 dB compression point (P1dB), saturation power, and power gain are achieved as 34 dBm, 36 dBm, and 38 dB, respectively. The power amplifier module consists of 16 unit power amplifiers which are arranged in a 4 × 4 array, and it is implemented to ensure the RF transmitter power of 48 W at 2.4 GHz. Since the gain of the designed power amplifier is 38 dB, its input power should be more than 0 dBm for the output power of 34 dBm. The power amplifier module, which consists of the RF power amplifier and transmitter antenna, is manufactured on a printed circuit board (PCB). A quasi-Yagi antenna is adopted as the transmitter antenna to satisfy both narrow-bandwidth and directional pattern characteristics for the long-range RF energy harvesting test module. The quasiYagi antenna has an operating bandwidth of 100 MHz from 2.4 GHz to 2.5 GHz and a gain of 6 dBi. In order to obtain the high gain, a 4 × 4 array is formed, in which the power amplifier module acts as a single element. The distance between the power amplifier modules is optimized as 8.5 cm to reduce grating lobes. Therefore, the overall size of the 4 × 4 power amplifier module is 34 cm × 34 cm. The drive amplifier is designed to amplify the signal source of 0 dBm, which is produced by a vector signal generator such as an E4438C, to the output power of 28 dBm. The driver amplifier is a single unit and the 4 × 4 power amplifier module 10 Mar 2017 at 07:57:49, .003

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RF Signal (Input = 10 dBm)

Drive Amplifier (Gain 22 dB power 28 dBm)

Power Amplifier Module Power Amplifier (Gain 38 dB, Each Power 34 dBm × 16EA)

2.4 GHz Energy Transfer

Receiving Antenna (Gain = 3 dBi)

Matching Circuit (Reflection < –10 dB)

RF/DC Converter

Battery Charger (Efficiency 70%, 4.2 V Charging)

Li-Ion Battery (100 mAh)

Figure 2.6 Block diagram of energy harvesting unit with the computed design target.

consists of 16 units, therefore, a 1-to-16 way power splitter is utilized between the driver amplifier and the 4 × 4 power amplifier module. The output power of the drive amplifier is determined by considering a required input power for the power amplifier of 0 dBm. A gain of ideal power splitter is about −12 dB, while −14 dB of minimum gain is obtained in the measurement. The minimum input power should be 14 dBm at least, to achieve an output power of the splitter of 0 dBm. In order to satisfy these requirements, an AVAGO ALM-81224 is used as the driver amplifier with a P1dB of 28 dBm and a gain of 24 dB. 10 Mar 2017 at 07:57:49, .003

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Figure 2.7 Schematic diagram of the designed drive amplifier.

In order to evaluate the performance of 2.4 GHz long-range RF energy harvesting test-bed for energy transfer efficiency with respect to distance, the physical distance between the transmitter and the receiver should be fixed. It is possible to realize such an environment by changing the output power of the power amplifier using the external control. The drive amplifier is employed for variation of the gain, instead of the power amplifier, which has a fixed gain. The range of the gain of the drive amplifier is from −15 dBm to 23 dBm. The output power of the drive amplifier is adjusted by external control such as an algorithm on a PC. Therefore, without changing the distance, we can still obtain the same results as the measured results with various physical distances between the transmitter and the receiver within the range 1–30 m. The system budget of the energy harvesting block in the receiver stage is computed based on the assumption of a 0 dBm input signal. According to the assumption, the input power is 1 mW. If the regulated voltage is 1 V, then the possible supplied current is 1 mA. This current level is acceptable for the energy harvesting block, even when losses such as mismatching of the receive antenna input, matching circuit, and RF-toDC conversion circuit have been considered. The designed drive amplifier and the fabricated drive amplifier are described schematically in Figures 2.7 and 2.8, respectively. The fabricated drive amplifier consists of a drive amplifier core block including input/output RF matching circuit, a bias circuit for supplying power to each stage of the drive amplifier, and a control block for controlling the output power of the drive amplifier. For the sake of stability, the main stage of the drive amplifier is designed for a fixed voltage of 5 V. To validate the overall efficiency, LDOs using variable resistors are applied to each stage to control the bias externally. 10 Mar 2017 at 07:57:49, .003

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Table 2.2. The bill of material (BOM) of the circuit shown in Figure 2.7 Part

Vendor

Description

ALM81224 LD2915 AZ1117CD R1, R2, R3 VR1, VR2, VR3 C1, C3, C4 C2 C5 C6 L1, L4 L2 L3

Avago STMicro Diodes Walsin Bourns Murata Murata Murata Murata CoilCraft CoilCraft CoilCraft

Power amplifier, 2.4 GHz, 28 dBm Fixed output LDO, 1.5 A Adjustable output LDO, 1 A 100 k, SMD, 1005 Variable resistor, 100 k 7.5 pF, SMD, 1005 1.0 pF, SMD, 1005 0.1 μF, SMD, 1005 2.2 pF, SMD, 1005 1.9 nH, SMD, 1005, 740 mA 5.6 nH, SMD, 1005, 740 mA 1.0 nH, SMD, 1005, 740 mA

Figure 2.8 The fabricated drive amplifier.

The measured gain and output power are 20 dB and 22 dBm, respectively. The degradation for a gain of 2 dB and for an output power of 2 dBm are observed by comparing the experimental data with the simulated results. The measured efficiency is 20%, and the measured power consumption of 5 V/384 mA is identical with the simulated result. Table 2.2 shows the bill of material (BOM) of the circuit given in Figure 2.7. Table 2.3 shows the results. The power amplifier block designed by employing an AVAGO MGA43024 is realized with the pattern antenna on a PCB. The power amplifier exhibits a gain of 38 dB, an 10 Mar 2017 at 07:57:49, .003

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Table 2.3. The measured result of the drive amplifier

Gain Output power Saturation power Gain range Power Efficiency

Simulation

Measurement

Note

22 dB 23.8 dBm 27.8 dBm 35 dB 5 V/380 mA 34%

20 dB 21 dBm 24 dBm 30 dB 5 V/384 mA 22.5%

At P1dB

Table 2.4. The BOM of the circuit shown in Figure 2.9 Part

Vendor

Description

MGA43024 LD2915 AZ1117CD R1, R2, R3 VR1, VR2, VR3 C1, C2, C4, C5 C3 TL1 TL2, TL3 TL4, TL5

Avago STMicro Diodes Walsin Bourns Murata Murata – – –

Power amplifier, 2.4 GHz, 34 dBm Fixed output LDO, 1.5 A Adjustable output LDO, 1.0 A 100 k, SMD, 1005 Variable resistor, 100 k 7.5 pF, SMD, 1005 8.2 pF, SMD, 1005 50 , 2.422 GHz, 7.0 degrees 50 , 2.422 GHz, 8.3 degrees 50 , 2.4 GHz

output power of 34 dBm, and a saturation power of 36 dBm. Figures 2.9 and 2.10 display schematic diagrams and the fabricated model of the designed power amplifier module, respectively. Table 2.4 shows the BOM of the circuit shown in Figure 2.9. By employing the designed power amplifier module as the single element of 4 × 4 array as shown in Figure 2.11, the power amplifier module exhibits an output power of 48 dBm. In order to not only prevent the coupling between power blocks but also enable the thermal dissipation, each power amplifier module is isolated in a shielded block. As illustrated in Figures 2.4 and 2.6, the energy harvesting unit in a receiver stage is composed of the input matching networks, RF-to-DC converter, DC–DC converter, and battery charger controller. The important circuits among these components include the RF-to-DC conversion circuit and input matching networks. The RF-to-DC conversion circuit composed of the Schottky diode has very low input impedance at 2.4 GHz. Most received signals are reflected without a matching network, thereby decreasing the harvesting efficiency. By applying the matching network, the degradation of the efficiency due to the impedance mismatching is prevented and the minimum detectable signal is improved to −20 dBm. In the design of the matching network, an AVAGO HSMS-286C Schottky diode is used. The Schottky diode has a forward voltage drop of 0.35 V and a forward capacitance of 0.25 pF [7]. In order to operate the RF-to-DC converter, the forward voltage drop of the diode and equivalent capacitance of the matching network should be low. 10 Mar 2017 at 07:57:49, .003

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Figure 2.9 Schematic diagram of the designed power amplifier module.

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Figure 2.10 The fabricated power amplifier module.

Figure 2.11 Configuration of the 4 × 4 power amplifier module.

These conditions lead to the regulation of low input power with good impedance matching and prevention of the reduction of the detection range. A matching network based on [6] and [7] has been designed. Figure 2.13 shows a schematic diagram of the 2.4 GHz energy harvesting circuit composed of the RF-to-DC converter circuit. This circuit includes a 1 V to 3.3 V boost DC– DC converter circuit and the C/L matching circuit based on the recommended matching network as shown in Figure 2.12. In the lower part of Figure 2.13, the ADP3334 LDO is designed to supply current to the load directly without charging the battery when battery charging by the boost DC–DC converter is impossible due to the current consumption at the load of the harvesting circuit. 10 Mar 2017 at 07:57:49, .003

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Table 2.5. The BOM of the circuit shown in Figure 2.13 Part

Vendor

Description

LTC3458 BQ2423 ADP3334 D1, D2 D3 C1 C2, C3 C4, C6 C5 L1 L2 R1, R2, R3, R9, R12, R13 R4, R7 R5 R6 R8 R10 R11

Linear TI TI Avago NXP Murata Murata Murata Murata Abracon CoilCraft Walsin Walsin Walsin Walsin Walsin Walsin Walsin

DC–DC boost converter Charge controller Adjustable output LDO Schottky diode, SMD Schottky diode, 0.3 V 18 pF, SMD, 1005 5 pF, SMD, 1005 10 μF, SMD, 1005 0.1 μF, SMD, 1005 6.2 nH, SMD, 2% 10 μH, SMD, 1.5A 100 k, SMD, 1005 150 k, SMD, 1005 124 k, SMD, 1005 133 k, SMD, 1005 82 k, SMD, 1005 360 k, SMD, 1005 200 k, SMD, 1005

Video Out

RF Input Width = 0.017” Length = 0.436”

100 pF

Width = 0.78” Length = 0.165” Transmission Line Dimensions Are for Microstrip on 0.032” Thick FR– 4 Figure 2.12 The recommended matching circuit of HSMS-286.

BQ24230 IC in Figure 2.13 is the charger IC, which is capable of operating in the low-current mode. In the situation that the load current increases in stand-alone mode, BQ24230 IC stops the battery charging function and supplies the current from the battery to the load automatically. When testing the operation of the energy harvesting system by connecting a data communication module to the load, it is possible to employ the battery efficiently without external control of the harvesting circuit.

2.2.2.3

Experimental Results The characteristics of the energy harvesting module are validated for 2.4 GHz longrange RF energy harvesting test-bed (Figure 2.14). Because the 50  matching network consists of an HSMS-286C Schottky diode, the minimum detectable signal and 10 Mar 2017 at 07:57:49, .003

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Figure 2.13 Schematic diagram of the designed RF-to-DC converter with matching network and DC–DC converter.

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Figure 2.14 The fabricated 2.4 GHz energy harvesting module.

Figure 2.15 Output voltage of the 2.4 GHz long-range RF energy harvesting module with different input powers.

available supply power to operate each system are confirmed for the system specification. Figure 2.15 delineates the regulated output voltage and DC–DC output voltage with variable input powers. As shown in Figure 2.15, the input power for generating regulation of the received signal is −20 dBm but a minimum input voltage of 0.7 V to operate the DC–DC converter is achieved by supplying the input power of −8 dBm. The minimum input power is determined as 0 dBm to produce the required DC–DC output voltage of 3.3 V for operating the system. The regulated output voltage and DC–DC output voltage with different distances between the 34 dBm (3 W) signal source and the receiver are illustrated in Figure 2.16. In the evaluation, a 34 dBm single power amplifier circuit is used instead of a 48 W output test board in order to ignore the effect of beamforming. Because the beamforming 10 Mar 2017 at 07:57:49, .003

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Figure 2.16 Output voltage of 2.4 GHz long-range RF energy harvesting module with different distances between the signal source and the receiver.

Figure 2.17 Efficiency of 2.4 GHz long-range RF energy harvesting module with different input

powers.

affects the characteristics of the output signal, it is difficult to validate the harvesting efficiency according to the output power. As shown in Figure 2.16, the regulated voltage is stable over the whole range of the distance between the signal source and the receiver, while the usable DC–DC output voltage of 3.3 V is supplied within a distance of 0.6 m. For distances from 0.9 to 1 m, the DC–DC converter generates an unsuitable output voltage. Therefore, the energy harvesting module can operate the system within a distance of 0.6m by employing a 34 dBm output signal. Figure 2.17 shows the efficiency of the energy harvesting module between the regulated output voltage and the input power. When the input power is lower than −12 dBm, it is possible to measure the regulated output voltage within 0.5 to 0.7 V. However, the 10 Mar 2017 at 07:57:49, .003

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Table 2.6. Measured results of the long-range RF energy harvesting module Parameter

Target

Measured result

Note

Frequency Receiver matching result Minimum detectable signal Minimum available signal Maximum power transfer distance Maximum available power transfer distance Efficiency Receiver output voltage Regulated voltage

2.45 GHz < −10 dB

2.45 GHz −8.4 dB

−20 dBm

−14 dBm

At 0.5 V

0 dBm

4 dBm

2m

2m

Receiver operation At 0.5 V

1m

0.8 m

38% 3.3 V

32% 3.3 V

1.8 V

1.3 V

Receiver operation

efficiency is 0% due to the unstable current. The efficiency is nearly 30% in the normal operation range when the current is about 300 μA. This low current is insufficient to apply directly to a wireless communications system without accumulating the current in the storage unit. Table 2.6 describes the measured results of the long-range RF energy harvesting module with unit-power amplifier. To improve the energy harvesting efficiency and the minimum level of detectable signal characteristics at 2.4 GHz, one must use a diode of lower threshold voltage than that of the common Schottky diode. Because the forward voltage drop of the Schottky diode is nearly 0.5 V, the regulated output voltage is almost 0.9 V using the ideal diode. In addition, the improvement of the matching circuit is necessary to enhance the energy harvesting efficiency and the level of minimum detectable signal.

2.2.3 2.2.3.1

Low-Power/Short-Range Test Module System Configuration The overall system block diagram of the low-power/short-range test-bed is shown in Figure 2.18. In the low-power/short-range test-bed, the energy harvesting and data communication are implemented using the frequency bands 915 MHz and 2.4 GHz, respectively, which are different from those of the high-power/long-range RF energy harvesting. The 2.4 GHz BLE standard is adopted for data communication, while the power transfer system is designed to transfer the energy, using 915 MHz on–off keying (OOK) modulation with the signal control always turned on. The 915 MHz transmitter is composed of the 915 MHz signal source, drive amplifier, and chip antenna. The 2.4 GHz BLE transceiver is one of the key blocks in the data communication module. The short-range test-bed uses different frequency bands for 10 Mar 2017 at 07:57:49, .003

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Control Module USB/RF Energy Harvesting

Charger

Battery Modulation (OOK, ASK)

PA

BLE Wireless Transceiver IC Tx Data Rx Data

Base Band Modem

Modulation Data PLL

PA

SPDT Base Band Analog

LNA

Communication (2.4 GHz BLE)

ADC

Energy Transfer (915 MHz ISM)

64

Human

Sensing Information (Ex, Temp, EEG, ECG)

Sensor Module

LDO

Rectifier

Bio Sensor Tx Data

Rx Data

Base Band Modem

BLE Wireless Transceiver IC Modulation Data PLL

PA

SPDT

ADC

Base Band Analog

LNA

Figure 2.18 Block diagram of the low-power/short-range test-bed.

energy transfer and data communication so that it can easily be extended to different standards such as ZigBee or Backscattering. The drive amplifier for the 915 MHz energy transfer is implemented using the commercial power amplifier to provide an output power level up to 28 dBm with a high power conversion efficiency of about 40%. The 915 MHz signal source is implemented by applying the 915 MHz signal directly from an external signal source such as an E4438C Vector Signal Generator to the module or 10 Mar 2017 at 07:57:49, .003

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2–3 m

Sensor TAG Include BLE Module 915 MHz Signal Transmitter and BLE Module

Figure 2.19 Implemented blocks.

using the self-signal generation circuit under the external supply voltage. The self-signal generation circuit is designed using the crystal oscillator and 915 MHz up-conversion mixer with the maximum output power of 5 dBm. The energy harvesting receiver stage is composed of a 915 MHz chip antenna, P2110 RF-to-DC power converter, DC–DC converter, and supercapacitor. Also, the energy harvesting module consists of the bio-sensor or data communication circuit. A commercial RF-to-DC power converter, P2110, with small area and user friendliness is adopted since the bio-sensor module needs to operate without an external power supply or batteries. The bio-sensor module transfers the data from the bio-sensor through the BLE. Since it needs to be attached to the human body as a type of patch, secondary batteries such as Li-ion or Li-NH cannot be used. Storage units such as supercapacitors can be used in the system instead of those. The DC–DC converter and LDO (low drop out) should have the minimum quiescent current for the required low-power operation. Figure 2.19 illustrates the implementation of the blocks which are shown in Figure 2.18.

2.2.3.2

Design The target specifications of the short-range energy harvesting module are determined based on the Friis equation in a similar way to the long-range RF energy harvesting. The maximum distance between the transmitter and the energy harvesting bio-sensor module is limited to 3 m. The power loss is calculated with respect to the distance assuming that the maximum output power is 30 dBm. The power loss will be about 42 dB assuming that the antenna gain is 0 dBi when the output power is 28 dBm and the distance 3 m. Table 2.7 summarizes the target specification with respect to the power, frequency, and distance based on the Friis equation. The output power of the RF transmitter, receiver antenna gain, and transmitter antenna gain are determined to be 28 dBm, 0 dBi, and 0 dBi at 915 MHz, respectively, as specified in Table 2.7, which result in a 10 Mar 2017 at 07:57:49, .003

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Table 2.7. Summary of the target specification based on Friis equation Parameter

Unit

Target

Note

Frequency Output power Target distance Receiver antenna gain Transmitter antenna gain Minimum required power

MHz dBm m dBi dBi dBm

915 28 2–3 0 0 −10

At receiver

SMA Connector

Path 2

Path 1

ALM32120 34 dBm, 50% 5 V/800 mA

Path 1: External 915 MHz RF Signal from Signal Source Path 2: External IF CW Signal from Signal Source Path 3: External IF CW Signal Using Oscillator

Transmitter Module Path 3 CW Reference Signal

Control :reset / power set

Transmitter Module Target

CW Reference Signal

Up-mixer with DA TH72035

Crystal Oscillator

: Up-mixer with DA – TH72035 / 915 MHz Melexis :Crystal – 28.59 MHz – 915 MHz :Reference IF – 82.786 kHz or MICOM Random Signal :Reference IF Buffer :Output Power Amplifier

Figure 2.20 Calculated block design target.

loss of 40 dB at a distance of 2.3 m. The distance is extended to 4.6 m by increasing the transmitter antenna gain, transmitter output power, and receiver antenna gain to 3 dBi, 30 dBm, and 3 dBi, respectively, in order to design the short-range energy harvesting efficiently. The internal signal generation circuit in the transmitter is implemented in Figure 2.20 using the TH72035 915 MHz FSK (frequency shift keying)/ASK (amplitude shift keying) transmitter IC [8] of Melexis and the ALM32120 2 W high-linearity amplifier of AVAGO. The TH72035 transmitter is adopted since it can be programmable as direct OOK modulation mode or FSK modulation mode through the external control. The frequency of the output signal is determined from the data sheet. The external crystal oscillator is used in this test-bed, whose output signal frequency is determined by 10 Mar 2017 at 07:57:49, .003

Circuit Design for Wireless Energy Harvesting

FOUT =

Fcrystal . 32

67

(2.2)

The output signal frequency of the transmitter is 915 MHz when the reference frequency of the crystal oscillator is 28.59375 MHz. The P1dB power, the saturation power, and the gain of the ALM32120 IC used as the drive amplifier are 2 W, 2.2 W, and 20 dB, respectively, with a power efficiency of about 40% for the P1dB power level. It is necessary to minimize the module size since input and output matching networks are embedded inside the IC. The module is implemented to support the OOK or FSK test of the data rate of around 1 Mbps through the PC using the external 915 MHz signal. The short-range test module has two functional test modes. First, the optimum duty cycle can be found by adjusting the duty cycle between energy harvesting time and data communication time using OOK modulation. Second, the feasibility of simultaneous energy harvesting and communication would be checked by changing the data communication circuit from BLE to the 915 MHz band and using OOK modulation. Generally, since data communication is possible with a minimum receiver sensitivity level of around −120 dBm in the case of OOK communication, data communication might be supported immediately with energy harvesting from the “On” signal. Figure 2.21 shows the schematic of the 915 MHz signal generation, transmitter, and 33 dBm power amplifier. The transmitter block is implemented to communicate with the external PC using the USB interface for the OOK modulation test. Table 2.8 shows the BOM of the circuit given in Figure 2.21. Figure 2.22 shows the design of the USB interface module. Figure 2.23 shows the implemented power transmitter module, which is composed of four parts, namely a USB interface module, a signal generation block, a transmitter IC, and a 2.4 GHz BLE module. Table 2.9 shows the BOM of the circuit given in Figure 2.22. The USB interface module with a PC is placed on the left. The signal generation block and transmitter IC are also placed in the schematic. The OOK modulation can be controlled directly as well as through the USB interface. The power amplifier is implemented to be connected to various antenna types using the SMA connector.

Figure 2.21 Schematic design of the 915 MHz signal generation circuit and power amplifier.

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Table 2.8. The BOM of the circuit shown in Figure 2.21 Part

Vendor

Description

TH72035 ALM32120 ECS-285 D1 L1, L2 C1 C2 R1, R2, R3 VR1 TL1, TL2

Melexis Avago ECS NXP TDK Murata Murata Walsin Bourns –

Up-converter with buffer, 915 MHz Power amplifier, 915 MHz, 28 dBm Crystal oscillator, 28.5938 MHz Zener diode, 5.5 V 6.8 μH, SMD, 2012, 0.5 A 12 pF, SMD, 1005 0.1 μF, SMD, 1005 100 k, SMD, 1005 Variable resistor, 100 k 50 , 2.4 GHz

Figure 2.22 Schematic design of the USB interface module.

Finally, the 2.4 GHz BLE module including the chip antenna is placed on the right. The nRF51822 IC of Nordic is adopted as the BLE module since it supports the pre-compiled driver and can reduce the power consumption by adjusting the timing of receive mode and transmit mode flexibly. The board is also designed to operate using the Coin battery for the stand-alone test. In particular, in the CW mode without OOK 10 Mar 2017 at 07:57:49, .003

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Table 2.9. The BOM of the circuit shown in Figure 2.22 Part

Vendor

Description

CY8C24894 TPS73701 AD5241 AP1117D50 ISSP L1 C1, C2 D1 D2, D3 R2, R3

Cypress TI Analog Device AnaChip Molex TDK Murata NXP Kingbright Walsin

8-bit MCU Fixed output LDO, 1.0 A 256-position digital potentiometers Fixed output LDO, 1.0 A 5-pin connector 6.8 μH, SMD, 2012, 0.5 A 0.1 μF, SMD, 1005 Zener diode, 5.5 V LED, SMD, 1005, 20 mA 330 , SMD, 1005

Figure 2.23 Implemented 915 MHz power transmitter module with 2.4 GHz BLE block.

modulation, it needs to be tested without the external supply since the external interface is not necessary. The energy harvesting module is composed of the energy harvesting circuit of 915 MHz frequency band and LDO. The P2110 module used as the energy harvesting circuit is implemented with diodes, being composed of the RF–DC converter block and the DC–DC converter block. It has a port for monitoring the internal output voltage and a 10 Mar 2017 at 07:57:49, .003

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VCAP

RFIN

Boost converter

RF to DC Converter

Voltage Monitor

GND

Vout VSET

INT RESET

DOUT DSET

Figure 2.24 Internal block diagram of the P2110 module.

Figure 2.25 Schematic design of the 915 MHz energy harvesting circuit.

final power output port. The output voltage of the P2110 module can be changed by the external resistor with the internal reference resistor. Since the supply voltage of the BLE for data communication IC in this test-bed is 3.3 V, the output voltage of the P2110 module is adjusted to 3.3–3.5 V. Ultra-low-dropout IC is added to the output of the P2110 module to provide the supply voltage to the BLE since the overall power efficiency of the module can be decreased if the external DC–DC converter is added in addition to the internal DC–DC converter in the P2110 module. Figure 2.24 shows the internal block diagram of the P2110 module. Figure 2.25 shows the energy harvesting circuit diagram of the 915 MHz frequency band. A chip antenna from Yageo is adopted to minimize the module size and a supercapacitor of 0.011 F is used instead of the battery. Table 2.10 shows the BOM of the circuit given in Figure 2.25. Figure 2.26 shows the finally implemented 915 MHz energy harvesting circuit.

2.2.4

Experimental Results The energy harvesting circuit of the 915 MHz frequency band uses a P2110 power harvesting circuit and is evaluated in a similar way to long-range RF energy harvesting. First, the normal operation of the P2110 device is checked in the implemented PCB 10 Mar 2017 at 07:57:49, .003

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Table 2.10. The BOM of the circuit shown in Figure 2.25 Part

Vendor

Description

P2110 ADP3334 C2 C1, C3 C4, C5 R1 R2 R3 R4

PowerCast TI Taiyo Yuden Murata Murata Murata Walsin Walsin Walsin

Energy harvesting module, 900 MHz Adjustable output LDO Supercapacitor, 0.011 F, SMD, 3225 10 μF, SMD, 1005 0.1 μF, SMD, 1005 4.3 M, SMD, 1005 100 k, SMD, 1005 150 k, SMD, 1005 82 k, SMD, 1005

Figure 2.26 Implemented 915 MHz energy harvesting module.

and the power level of the minimum detectable signal is measured to characterize the short-range system. The regulated voltage in Figure 2.27 shows the output voltage of the P2110 device. Figure 2.27 shows that the energy harvesting device with the P2110 module generates a normal output voltage when the input power level is above 3 dBm. Although the minimum input power level for normal operation is specified as −9 dBm in the P2110 data sheet [9], energy harvesting starts to operate for the input power level of −4 dBm and generates the required output level for an input power level of 3 dBm. Since the minimum input power level for stable operation is specified as 0 dBm, the measurement results agree well with the data sheet, considering the loss of the implemented PCB and matching with the antenna. The regulated output voltage is measured with respect to the distance between the energy harvesting circuit and the 915 MHz signal source. The purpose of this experiment is to check how far the energy harvesting circuit can be dislocated from the 10 Mar 2017 at 07:57:49, .003

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Figure 2.27 Measurement results of the energy harvesting circuit in the 915 MHz sensor module.

Figure 2.28 Interlocked measurement results with respect to the distance between the 915 MHz sensor module and the transmitter module for a transmitter power level of 23 dBm.

signal source and whether other communication methods such as backscattering can be used. Figure 2.28 shows the interlocked measurement results with respect to the distance between the 915 MHz sensor module and the transmitter module. From the measurement results, the P2110 energy harvesting circuit starts normal operation at a received signal level of −7 dBm, considering the loss of 30 dB at a distance of 0.8 m when the output power level of the transmitter module is 23 dBm and there is no antenna mismatch. However, the output of the DC–DC converter in the P2110 energy harvesting circuit reaches the normal supply voltage when the received input power level is 2 dBm at a distance of 0.3 m. Even though the distance is about 1 m for the harvesting circuit 10 Mar 2017 at 07:57:49, .003

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Table 2.11. Summary of measurement of the short-range test-bed module

Output voltage Efficiency Minimum detectable signal Maximum available distance

Simulation

Measurement

Note

3.3 V 40% −9 dBm

3.3 V 30%–33% −5 dBm

Normal operation

0.5 m

0.3 m

At 23 dBm output power

Figure 2.29 Measured efficiency of the 915 MHz sensor module.

itself, it can be reduced to 0.3 m due to the power consumption of other building blocks such as DC–DC converter circuits in practice. The gap with the theoretical value can be reduced by minimizing the loss due to mismatch with the antenna and improving the antenna gain, which can increase the output power of the transmitter module and distance to 30 dBm and 2 m, respectively. Figure 2.29 shows the measured overall efficiency of the 915 MHz energy harvesting system. It is calculated for the regulated voltage range of normal operation and is slightly degraded for the input power level of 4 dBm since the DC–DC converter starts to operate and consumes the power. Figure 2.29 shows the measured efficiency of 915 MHz sensor module. The maximum efficiency can be theoretically estimated to be about 40%, considering the maximum efficiency of the P2110 module of 55% [10] and the efficiency of the voltage conversion circuit of about 80% [11]. However, the measured efficiency ranges from 30% to 33% for most input levels and about 25% for a low input power level. The overall efficiency of the energy harvesting circuit is degraded since another voltage conversion circuit is added to meet the external supply voltage level in addition to the boost DC–DC converter in the P2110 power harvesting module. Table 2.11 summarizes the measured performance of the short-range test-bed module. 10 Mar 2017 at 07:57:49, .003

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2.3

Stored Energy Evolution Model for an IoT Sensor Node with Wireless Energy Harvesting Capability

2.3.1

IoT Sensor Node with Wireless Energy Harvesting Capability The IoT is the most promising application area of wireless energy harvesting since IoT sensor nodes are generally sustainable by a relatively small amount of energy provision. Much research has been conducted on energy harvesting sensor networks. Most of this work has focused on designing an algorithm to control sensor node parameters, e.g., duty cycle and data transmission power, to extend the lifetime of sensor nodes. A sensor node stores the harvested energy in an energy storage device such as a rechargeable battery or a supercapacitor, and the stored energy is later used for computation or communication. The energy storage device is able to supply energy for a while when no energy is being harvested. Therefore, the energy storage works as a buffer to mitigate the randomness of an energy arrival process. A smart energy management algorithm should be used to avoid depleting the energy storage while providing a certain qualityof-service (QoS) level. The energy management algorithm usually makes use of a temporal evolution model of the stored energy. A discrete-time temporal evolution model is generally given by Et+1 = min{max{Et − Ut , 0} + Ht , Emax },

(2.3)

where Et is the stored energy at time epoch t, Emax is the maximum energy that can be stored in the energy storage, Ut is the energy consumed at time epoch t, and Ht is the energy harvested at time epoch t. The energy management algorithm can stochastically predict the harvested energy Ht in the future time epochs and accordingly control parameters affecting the consumed energy Ut to achieve a certain performance target. The temporal evolution model of the stored energy in (2.3) can be applied to a sensor node with wireless energy harvesting as well. However, the property of the wireless energy harvester should first be characterized for fully modeling the energy harvesting process Ht . Moreover, this evolution model is an ideal model based on the energy conservation law. However, in a real system, some energy can be lost in the process of harvesting, storing, and consuming energy because of the imperfection of the circuit components. Therefore, an appropriate circuit model is required in order to derive a more realistic temporal evolution model of the stored energy. Figure 2.30 shows a circuit system model of a sensor node equipped with wireless energy harvesting capability. This model consists of three hardware modules: a wireless energy harvesting board, a supercapacitor, and a sensor board. The radio-frequency (RF) power is received by the wireless energy harvesting board and is converted to direct current to supply energy to the sensor node. A supercapacitor is used as an energy storage device. The harvested energy is stored in the supercapacitor when more energy is harvested than the energy consumed by the sensor board. The sensor board obtains sensing results, performs computation, and sends the sensing results to other devices. For this operation, the sensor board consumes the energy harvested by the wireless energy harvesting board. 10 Mar 2017 at 07:57:49, .003

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The wireless energy harvester generally consists of a matching network, a rectifier, and a DC–DC converter. The performance of the wireless energy harvester depends on how these components are designed. Owing to the nonlinearity of these components, it is very difficult to derive a meaningful analytic expression for describing the behavior of the wireless energy harvester. Rather than modeling each component of the wireless energy harvester, a current–voltage curve (i.e., an I–V curve) according to a given received signal strength (RSS) can be used for fully characterizing the wireless energy harvester. The I–V function of the wireless energy harvester can be defined as IEH = λ(VEH , RSS),

(2.4)

where RSS is the RSS of the microwave signal incident on the antenna of the wireless energy harvester, and Vcap and Icap are the voltage and the current of the wireless energy harvester, respectively. A supercapacitor is considered a suitable energy storage device for energy harvesting sensor nodes since it can endure rapid charging and discharging cycles. As shown in Figure 2.30, a supercapacitor is typically modeled by an ideal capacitor, a leakage resistor, and an equivalent series resistor (ESR). The ideal capacitor has a capacitance of C. The derivative of the voltage of the ideal capacitor is proportional to the current since dVcap Icap = , dt C

(2.5)

where Vcap and Icap are the voltage and the current of the ideal capacitor, respectively. The energy stored in the ideal capacitor is Ecap =

1 2 CV . 2 cap

Figure 2.30 IoT sensor node model with wireless energy harvesting capability.

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(2.6)

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A leakage resistor and an ESR are introduced to describe the non-ideal behavior of a real supercapacitor. A supercapacitor discharges by itself even when it is disconnected from other parts of the circuit. If the resistance of the leakage resistor is Rleak , the leakage current is Ileak = Vcap /Rleak . The ESR is placed in series with the ideal capacitor to model the inherent resistance of the supercapacitor. The resistance of the ESR is RESR . Therefore, the supercapacitor under consideration is fully characterized by three parameters: the capacitance C, the leakage resistance Rleak , and the equivalent series resistance RESR . The sensor board acts as a load that draws energy from the wireless energy harvester and the supercapacitor. The main energy sinks in the sensor board are integrated circuits (ICs) such as the processor and the communication chip. In the sensor board, the processor is usually a micro-controller unit (MCU) and the communication chip is compliant to a low-power communication standard such as IEEE 802.15.4. The ICs on the sensor board acts as different types of loads depending on how they consume energy. Two types of loads are incorporated in this model: a constant-resistance load and a constantcurrent load. Typically, the sensor board alternates between several different modes: idle, active, receive, and transmit. Almost all the ICs are turned off except for minimal functionalities (e.g., timer) in the idle mode, the processor is activated in the active mode, the communication chip is ready to receive data in the receive mode, and the communication chip transmits data in the transmit mode. Each mode has different load characteristics. When the sensor board is in mode m, the resistance of the constantresistance load and the current of the constant current load are denoted by γ (m) and ζ (m), respectively.

2.3.2

Wireless Energy Harvesting Test-Bed and Measurement Result The stored energy evolution model can be set up if all related parameters in the sensor node model in (2.30) (i.e., λ, C, Rleak , RESR , γ (m), and ζ (m)) are identified. To this end, a real-life test-bed is set up and all relevant parameters are measured. This test-bed consists of a power beacon, which is able to wirelessly send energy via microwaves, and a sensor node, which makes use of the energy received from the power beacon. Only offthe-shelf commercially available hardware components are used to build the test-bed, and the test-bed is controlled by software so that various energy and data transmission experiments can easily be conducted. In the power beacon, we use a laptop connected to the universal software radio peripheral (USRP) [12] and power amplifier (i.e., Mini-Circuits ZHL-5W–422+ [13]), instead of using a static power transmitter with a fixed signal and power. Thereby, we can dynamically adjust the waveform and the power on the transmitter side. In a sensor node, a sensor board (i.e., Zolertia Z1 mote [14]) draws current from a supercapacitor (i.e., Samxon DDL series) that stores the energy charged by an energy harvesting board (i.e., Powercast P1110 [15]). The energy transmission part of the power beacon consists of a USRP, an amplifier, and an antenna. The USRP is controlled by software running on the laptop computer and works as an RF signal generator. However, the signal generated by the USRP is 10 Mar 2017 at 07:57:49, .003

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too weak (i.e., approximately 100 mW at maximum) to be used for wireless energy transfer. Owing to signal fading, a high-power RF signal is necessary in order to be able to transfer sufficient power to the sensor node. In order to accomplish this goal, a power amplifier that can provide up to 5 W transmit power is selected and a directional antenna is used to focus the microwave signal in the intended direction. The sensor node in the test-bed consists of a wireless energy harvesting board, a supercapacitor, and a sensor board with the same arrangement as in (2.30). The energy harvesting board (i.e., Powercast P1110) has an internal power meter and is capable of measuring the RSSs. The sensor board (i.e., Zolertia Z1 mote) can acquire the RSS from the energy harvesting board by using analog-to-digital conversion (ADC). The sensor board can also measure the voltage level of the supercapacitor, which indicates the amount of the energy stored in the supercapacitor. The sensor board adopts TI MSP430 as an MCU and TI CC2420 as a communication chip. The power beacon and the sensor node exchange information by means of the IEEE 802.15.4 transceiver. In the sensor node, the IEEE 802.15.4-compliant chip (i.e., TI CC2420) in the sensor board is used for communication. On the other hand, in the power beacon, another USRP or another sensor board attached to the laptop via serial connection can be used for communication. By using this communication link, the sensor node can report the RSS or the voltage level of the supercapacitor to the power beacon. The power beacon can send a command to the sensor node via this communication link, too. In this test-bed, tests on the P1110 wireless energy harvester are conducted and the current–voltage curve is obtained for various RSSs. An electronic load is utilized to obtain the current at various voltages. Figure 2.31 shows the measurement result of the I–V curve of the P1110 wireless energy harvester. The graphs in Figure 2.31 are drawn for various RSSs ranging from −4 dBm to 10 dBm. This figure defines the I–V function

Figure 2.31 Current supply of the P1110 wireless energy harvester according to the voltage.

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12 11 10 9

RSS: –4 dBm RSS: –3 dBm RSS: –2 dBm RSS: –1 dBm RSS:0 dBm

RSS: 1 dBm RSS: 2 dBm RSS: 3 dBm RSS: 4 dBm RSS: 5 dBm

RSS: 6 dBm RSS: 7 dBm RSS: 8 dBm RSS: 9 dBm RSS: 10 dBm

8 Power (mW)

78

7 6 5 4 3 2 1 0 0.6 0.8 1.0

1.2

1.4

1.6

1.8 2.0 2.2 2.4 2.6 2.8

Voltage (V) Figure 2.32 Power of the P1110 wireless energy harvester according to the voltage.

λ in (2.4) and can be directly used for analysis. However, a shortcoming of this approach is that a closed-form analytic result cannot be derived. Figure 2.32 shows the power–voltage graph of the P1110 wireless energy harvester. In this figure, the harvested power is stable in the range of 2.0 to 2.8 V thanks to the power management of the P1110 wireless energy harvester. Since this range corresponds to the operating voltage range of the sensor board, it is possible to make the assumption that the harvested power is invariant over the voltage range of interest. Let ρ(RSS) denote the harvested power for a given RSS, which is not a function of the voltage. Then, the I–V curve is IEH = λ(VEH , RSS) = −

ρ(RSS) . VEH

(2.7)

The efficiency of the wireless energy harvester is defined as the ratio of the harvested power to the received power, that is, η(RSS) =

ρ(RSS) . RSS

(2.8)

From the I–V curve, the efficiency graph is plotted as in Figure 2.33 as a function of the RSS. As discussed above, the voltage does not have a significant impact on the efficiency in the range 2.0 to 2.8 V. Therefore, the average efficiency graph in Figure 2.33 can safely be used for determining the efficiency according to the RSS. Finally, the relationship between the current and the voltage is rewritten as IEH VEH = −ρ(RSS) = −η(RSS) · RSS.

(2.9)

The parameters of the supercapacitor are obtained in the test-bed as well. The testbed uses a Samxon DDL series supercapacitor with a capacitance of C = 0.1 F. In Figure 2.34, a leakage test is conducted by letting the supercapacitor discharge by 10 Mar 2017 at 07:57:49, .003

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Figure 2.33 Efficiency of the P1110 wireless energy harvester. 3.3 3.2

Voltage (V)

3.1 3.0 2.9 2.8 2.7 2.6 2.5 0

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time (seconds)

Figure 2.34 Leakage of the supercapacitor.

itself. The ideal capacitor and the leakage resistor in Figure 2.30 form an RC circuit when disconnected from other parts. The voltage of an RC circuit evolves according to the following equation   t V(t) = V0 exp − , (2.10) Rleak C where V(t) is the voltage at time t and V0 is the initial voltage at time t = 0. By fitting (2.10) to the graph in Figure 2.34, the leakage resistance is obtained as Rleak = 196 k. In addition, the resistance of the ESR is tested by the following 10 Mar 2017 at 07:57:49, .003

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Table 2.12. Modes of ICs for each state in the Z1 mote IC

Idle

Active

Receive

Transmit (−25 dBm)

Transmit (0 dBm)

MSP430 CC2420

LPM3 OFF

AM OFF

AM Receive

AM Transmit (−25 dBm)

AM Transmit (0 dBm)

Figure 2.35 Current consumption of the Z1 sensor board according to the voltage.

method. The supercapacitor is first discharged at a constant current while the voltage is measured. Then, discharging is stopped and the voltage is measured again. From these two voltage measurements, the resistance of the ESR is obtained as RESR = 4.9 . In the test-bed, the Zolertia Z1 mote is used as a sensor board. We test the load characteristics of the Z1 mote for different modes of the sensor board. The test is done for the following five modes: idle, active, receive, transmit (−25 dBm), and transmit (0 dBm). The states of the processor (i.e., MSP430) and the communication chip (i.e., CC2420) decide the mode of the sensor board. Table 2.12 shows the states of the MSP430 and the CC2420 for each mode. In the idle mode, the MSP430 is in a lowpower mode (i.e., LPM3) and the CC2420 is in the OFF state. In this mode, the MSP430 and the CC2420 become inactive and the power consumption of those ICs is almost negligible (i.e., around 0.1 μW). In the active mode, the MSP430 is in the active mode (AM) with 8 MHz clock speed and the CC2420 is still in the OFF state. In this mode, the MSP430 can execute instructions but no data communication is available. In the receive mode, the CC2420 is in the receive state and the sensor board is able to receive data from other devices. The CC2420 sends a data packet in the transmit mode. Two transmit modes with different transmit powers (i.e., −25 dBm and 0 dBm) are tested. In Figure 2.35, the current consumption of the Z1 mote is measured according to the voltage. In the idle mode, a very small current consumption (i.e., 0.02 mA) is observed 10 Mar 2017 at 07:57:49, .003

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Table 2.13. Measured parameters of the constant-resistance and constant-current loads for each state in the Z1 mote Load type

Idle

Active

Receive

Transmit (−25 dBm)

Transmit (0 dBm)

CRL CCL

0 0.02 mA

0.68 k 0.02 mA

0.68 k 18.86 mA

0.68 k 9.19 mA

0.68 k 19.35 mA

because of the leakage current of the ICs on the sensor board. In the active mode, the current consumption is proportionally increased with respect to the voltage. This is because the MSP430 acts as a constant-resistance load. The load resistance of the MSP430 in the AM is calculated to be 0.68 k. In the receive and transmit modes, the CC2420 is in the receive and transmit states while the MSP430 is in the active mode. The current consumption of the CC2420 is obtained by subtracting the current consumption of the MSP430 from the measured current consumption. The CC2420 acts as a constant-current load and the current consumption of the CC2420 is calculated to be 18.86 mA in the receive state, 9.19 mA in the transmit state (−25 dBm), and 19.35 mA in the transmit state (0 dBm). These results are summarized in Table 2.12. From this table, the resistance of the constant-resistance load (CRL) (i.e., γ (m)) and the current of the constant-current load (CCL) (i.e., ζ (m)) are decided for each mode m.

2.3.3

Stored Energy Evolution Model In Section 2.3.2, all the parameters for the circuit model in Figure 2.30 have been identified on the wireless energy harvesting test-bed. This section introduces the derivation of the ordinary differential equation (ODE) that governs the evolution of the stored energy. Once this ODE has been mathematically derived, the measured parameters are put into the ODE and this ODE fully describes the evolution of the stored energy. The resistance of the ESR, the leakage resistor, and the constant-resistance load are denoted by RESR , Rleak , and RCRL , respectively. The capacitance of the capacitor is denoted by C. The voltages and currents of the wireless energy harvester, the capacitor, the ESR, the leakage resistor, the constant-resistance load, and the constant-current load are denoted by VEH , IEH , Vcap , Icap , VESR , IESR , Vleak , Ileak , VCRL , ICRL , VCCL , and ICCL , respectively. According to Kirchhoff’s law, the following equalities hold for the voltages and currents in the circuit model in Figure 2.30: VEH = VESR + Vcap = VCRL = VCCL ,

(2.11)

Vcap = Vleak ,

(2.12)

IEH + IESR + ICRL + ICCL = 0, IESR = Icap + Ileak . 10 Mar 2017 at 07:57:49, .003

(2.13) (2.14)

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From (2.7), the relationship between VEH and IEH is VEH IEH = PEH = −ρ(RSS),

(2.15)

where PEH is the power of the wireless energy harvester. Moreover, the resistance of the constant-resistance load depends on the mode of the sensor board. That is, RCRL = γ (m),

(2.16)

where γ (m) is the resistance of the constant-resistance load when the mode of the sensor board is m. Similarly, the current of the constant-current load depends on the mode of the sensor board according to ICCL = ζ (m),

(2.17)

where ζ (m) is the current of the constant-current load when the mode of the sensor board is m. From (2.11), (2.13), (2.15), (2.16), and (2.17), the voltage VEH is VEH = VESR + Vcap = IESR RESR + Vcap = −(IEH + ICRL + ICCL )RESR + Vcap   ρ(RSS) VCRL = − − ζ (m) RESR + Vcap . VEH γ (m)

(2.18)

From (2.18), a quadratic equation of VEH is formulated as 2 VEH −

γ (m)(Vcap − ζ (m)RESR ) ρ(RSS)γ (m)RESR VEH − = 0. γ (m) + RESR γ (m) + RESR

The solution to (2.19) is ⎛ 1 ⎝ γ (m)(Vcap − ζ (m)RESR ) VEH = 2 γ (m) + RESR ⎞    γ (m)(Vcap − ζ (m)RESR ) 2 ρ(RSS)γ (m)RESR ⎠ . + +4· γ (m) + RESR γ (m) + RESR

(2.19)

(2.20)

By the Taylor series expansion, VEH is VEH =

γ (m)(Vcap − ζ (m)RESR ) ρ(RSS)RESR + + , Vcap − ζ (m)RESR γ (m) + RESR

(2.21)

where =

∞  k=2

wk

4k ρ(RSS)k RkESR (γ (m) + RESR )k−1 . γ (m)k−1 (Vcap − ζ (m)RESR )2k−1

(2.22)

In (2.22), wk is wk =

 k  1 1 −i+1 . k! 2 i=1

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(2.23)

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The voltage and current around the ESR are VESR = VEH − Vcap RESR Vcap ρ(RSS)RESR γ (m)RESR ζ (m) = − + + , Vcap − ζ (m)RESR γ (m) + RESR γ (m) + RESR IESR = VESR /RESR Vcap ρ(RSS) γ (m)ζ (m) = − − + . Vcap − ζ (m)RESR γ (m) + RESR γ (m) + RESR RESR

(2.24)

(2.25)

The current through the capacitor is calculated as Icap = IESR − Vcap /Rleak Vcap Vcap ρ(RSS) γ (m)ζ (m) = − − − + . (2.26) Vcap − ζ (m)RESR γ (m) + RESR Rleak γ (m) + RESR RESR The voltage of the capacitor varies over time according to the following rule: dVcap Icap = , dt C

(2.27)

where C is the capacitance of the capacitor. The energy stored in the capacitor is calculated from Ecap =

1 2 CV . 2 cap

(2.28)

The power charged to the capacitor is dEcap = Vcap Icap dt 2 2 Vcap Vcap Vcap = ρ(RSS) − − Vcap − ζ (m)RESR γ (m) + RESR Rleak Vcap γ (m)ζ (m) − Vcap + γ (m) + RESR RESR  2Ecap /C Ecap 2 2 Ecap = ρ(RSS) − − C γ (m) + R C Rleak 2Ecap /C − ζ (m)RESR ESR  2 γ (m)ζ (m)  − Ecap + , C γ (m) + RESR

(2.29)

where is

 ∞ k−1 2E /C  4k ρ(RSS)k Rk−1 Vcap cap ESR (γ (m) + RESR ) 

= = wk . k−1 2k−1 RESR γ (m) ( 2Ecap /C − ζ (m)RESR )

(2.30)

k=2

The stored energy (i.e., Ecap ) evolves over time according to the ordinary differential equation (ODE) in (2.29). However, this ODE is nonlinear and too complex to be used for analysis. The ODE in (2.29) can be greatly simplified by removing the constant-current load from the equation. The removed constant-current load should be 10 Mar 2017 at 07:57:49, .003

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replaced by a similar constant-resistance load. If the constant-current load is removed (i.e., ζ (m) = 0), the ODE becomes   dEcap 1 2 1 + (2.31) = ρ(RSS) − Ecap + , dt C γ (m) + RESR Rleak where is

=

∞  k=2

wk

k−1 Ck−1 4k ρ(RSS)k Rk−1 ESR (γ (m) + RESR ) −(k−1) Ecap . γ (m)k−1

(2.32)

The ODE in (2.31) is simple but it is still not a linear ODE because of the term . Under the assumption that RESR is very small, can be omitted and the ODE becomes a linear one,   dEcap 1 2 1 + (2.33) = ρ(RSS) − Ecap . dt C γ (m) + RESR Rleak This ODE can be considered as a continuous-time version of the discrete-time temporal evolution model of the stored energy in (2.3).

2.4

Summary We have implemented and demonstrated two test-beds for RF energy harvesting. On the one hand, for high-power/long-range applications which use the 2.4 GHz ISM band, simultaneous operation for energy harvesting and data communication was successfully demonstrated within a distance of 1 m with a single power amplifier module. If 16 power amplifiers were fully deployed as planned, the distance would be increased to about 5 m. On the other hand, for low-power/short-range applications which use the 915 MHz ISM band for energy harvesting and the 2.4 GHz band for data communication, shortrange energy harvesting and data communication was successfully demonstrated at a distance of about 50 cm in spite of the limited transmit power and the considerable current consumption of other circuitry. If the matching between the antenna and the RF-to-DC converter and the transmit power were improved, the operational range could be improved to about 2 m. Although both long-range and short-range test-beds still have some parts to be further optimized or improved, the two test-beds can be utilized to develop RF energy harvesting circuits and methods for optimum operation of simultaneous RF energy harvesting and data communication. As the RF energy harvesting systems, these long- and shortrange test-beds can provide various useful experimental data for further studies and research in the RF energy harvesting area. In addition, we have developed the stored energy evolution model through experiment, modeling, and analysis using the test-bed, which will enable us to predict the temporal energy state in the energy storage device of an IoT sensor. With the evolution model, we will be able to devise a duty-cycle-based energy management algorithm for 10 Mar 2017 at 07:57:49, .003

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the IoT sensor which minimizes the transmit power from the dedicated energy source (e.g., power beacon) while avoiding occasional energy shortages in the energy storage device.

References [1] X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z. Han, “Wireless charging technologies: Fundamentals, standards, and network applications,” IEEE Communications Surveys and Tutorials, vol. 18, no. 2, pp. 1413–1462, second quarter 2016. [2] X. Lu, P. Wang, D. Niyato, D. I. Kim, and Z. Han, “Wireless networks with RF energy harvesting: A contemporary survey,” IEEE Communications Surveys and Tutorials, vol. 17, no. 2, pp. 757–789, second quarter 2015. [3] Powercast (www.powercastco.com). [4] Cota system (www.ossiainc.com). [5] C. Merz, G. Kupris, and M. Niedernhuber, “A low power design for radio frequency energy harvesting applications,” in International Symposium on Wireless Systems, 2014, pp. 443–461. [6] K. Gudan, S. Chemishkian, J. J. Hull, S. J. Tomas, J. Ensworth, and M. S. Reynolds, “A 2.4 GHz ambient RF energy harvesting system with −20 dBm minimum input power and NiMH battery storage,” in Proc. IEEE International Conference on RFID-Technology and Applications (RFID-TA), 2014, pp. 7–12. [7] HSMS-286 Schottky Diode datasheet (www.avagotech.com/docs/AV02-1388EN). [8] TH72035 Datasheet (www.melexis.com/General/General/TH72035-131.aspx). [9] K. Gudan, S. S. Shao, J. J. Hull, J. Ensworth, and M. S. Reynolds, “Ultra-low power 2.4 GHz RF energy harvesting and storage system with −25 dBm sensitivity,” in Proc. IEEE International RFID Conference, San Diego, CA, April 2015, pp. 40–46. [10] P2110 Product Datasheet (www.powercastco.com/PDF/P2110-datasheet.pdf). [11] LTC3458 Low Quiescent Current DC–DC Converter (http://cds.linear.com/docs/en/ datasheet/3458Lfa.pdf). [12] National Instruments, “NI USRP-292x/293x Datasheet: Universal Software Radio Peripherals” (www.ni.com/datasheet/pdf/en/ds-355). [13] Mini-Circuits, “Coaxial High Power Amplifier: ZHL-5W-422+” (www.minicircuits.com/ pdfs/ZHL-5W-422+.pdf). [14] Zolertia, “Z1 datasheet” (http://zolertia.sourceforge.net/wiki/images/e/e8/Z1_RevC_ Datasheet.pdf). [15] Powercast Corporation, “Product Datasheet: P1110 15 MHz RF Powerharvester Receiver” (www.powercastco.com/PDF/P1110-datasheet.pdf).

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3

Antennas for Wireless Energy Harvesting and Massive MIMO Applications Zahra A. Pour, Lotfollah Shafai, Ali M. Mehrabani, and Navid Rezazadeh

3.1

Introduction In conventional wireless and microwave communications, voice or data signals are exchanged between the users, suppliers, or both. The wireless communications need not be limited to information signals alone. Power can also be transmitted or exchanged. This possibility will extend the use of wireless systems to many new applications, simplify hardware designs, and remove the current requirement of wireless communication channels for locations with available power, or batteries. The latter places severe limitations on the use of wireless networks and prevents innovation in the related technologies and applications. In addition, the availability of wireless power will expand the use of wireless sensors to many new areas in remote sensing and medicine. It will also enable innovations in non-communication-related technologies such as transportation, unmanned aerial vehicles, and mechanical systems. The technology of wireless power transmission is currently known as microwave power transmission (MPT), or “energy harvesting.” While the former deals with any wireless power transmission, the latter refers mostly to small power levels. Historically, MPT has dealt with large power transmissions. Small power transmissions were not considered, mostly because wireless devices were not widespread and the power requirements of electronic devices were large. However, many new devices and technologies need small power levels to operate. Thus, energy harvesting is currently the primary area of interest, and this chapter will address the antenna designs for its applications, in particular antennas that can share both power and communication channels concurrently. However, since most research in the literature deals with communication antennas, for completeness a historical background is provided, to review the steps in the development of MPT, and the role of the antennas in its development. This is followed by a review of different antenna types that are useful for both energy harvesting and communications, and a few design examples. In selecting the design examples effort is made to choose antennas with low-profile structures, having geometries compatible with technologies for both passive and active Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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devices, mass production techniques and low-cost fabrication. In addition, since most innovations in communication, remote sensing and medical applications deal with small sizes, the design examples are selected to have potential for antenna miniaturizations. However, the actual antenna miniaturization techniques are not discussed in this chapter. Instead, we introduce and discuss design examples that can be scaled in size, without performance degradation. This is important, since the technology innovations cover both lower and upper microwave bands, and size scalable universal designs can be most useful for these applications. On the other hand, the size of resonant antennas is wavelength dependent and changes with the operating frequency. For this reason, in the selected designs the antenna centre frequency is assumed to be 1 GHz, and the substrate permittivity is considered to be unity. Thus, the proposed designs can easily be scaled to any frequency band, simply by dividing the proposed antenna dimensions by the required frequency of operation in GHz, without degradation of their impedance or radiation properties. These assumptions do not exclude other designs, or different permittivity values for the antenna substrates. However, in such cases the size scaling using frequency wavelengths may not be feasible and selected antennas must be designed using appropriate mathematical modeling. Integrating the energy harvesting with communication channels adds further requirements to the antenna designs. Some important areas are the antenna bandwidth, efficiency, antenna diversity, and the requirements of massive multiple-input, multipleoutput (massive MIMO) operating scenarios. To address the antenna impedance bandwidth, designs for both narrowband and wideband operation are provided. In all designs, the antenna efficiency is maximized by eliminating the lossy dielectric material. Then the case of antenna diversity is considered, and designs for incorporating both radiation pattern and polarization diversity are provided and discussed. A novel design with capability for dual diversity operation is also provided and investigated. Finally, the case of massive MIMO is also investigated. Sample array designs, based on two different antenna elements, are provided, and the influence of beam scanning on the array gain is discussed.

3.2

Historical Overview on Wireless Power Transmission In the late nineteenth century, wireless power transmission was first demonstrated by Heinrich Hertz [1], using a spark gap and dipole antennas in the UHF band. Around the dawn of the twentieth century, Nikola Tesla [2] successfully proved the concept by demonstrating his famous “Tesla coil” to wirelessly transmit electrical power, in Colorado Springs, CO, USA. Later, his Wardenclyffe Tower facility was constructed for wireless electrical power transmission over large distances, which did not become operational due to funding limitations. For security reasons, the facility was eventually dismantled during World War I. In the 1930s, another experiment was attempted by H. V. Noble at the Westinghouse Laboratory, where two identical 150 MHz dipole antennas were used to transmit power over a distance of 25 ft [3]. However, the research on wireless power transmission was brought to a halt until after World War II, mainly due to the low power-handling capacity of existing sources at high frequencies and the

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spillover loss of the then radiating elements. The former issue was resolved with the advent of high-power microwave vacuum tubes, such as velocity-modulated tubes [4], now known as klystron tubes, and microwave cavity magnetrons [5, 6], in the late 1930s and early 1940s. During World War II, significant developments and breakthroughs were made on the latter issue of antennas, which is the main focus of this chapter. In 1959, the Raytheon Airborne Microwave Platform (RAMP) was proposed for surveillance and communication applications, for which a large helicopter needed to be flown at altitude 50,000 ft and remotely powered from the ground by a high-power Amplitron at a frequency of 3 GHz. William Brown from the Raytheon company, who is now known as the principal pioneer of practical microwave power transmission, developed the required Amplitron at Raytheon’s Spencer Laboratory in 1960 [7]. The main issue was the conversion of AC to DC power, which was studied by R. George and E. Sabbagh at Purdue University in 1963, using semiconductor diodes as rectifiers [8]. Later, in 1968, thermionic diode rectifiers were studied by W. Brown [9]. All the aforementioned developments on high-power microwave sources and rectifiers made the microwave power transmission technically viable. The concept was successfully demonstrated for the first time on July 1, 1964, using a microwave-powered helicopter at 2.45 GHz, flown near the ground at Raytheon’s Spencer Laboratory. Later on October 28, 1964, the experiment was repeated, this time at altitude 50 ft, using dipole antennas and semiconductor diode rectifiers [10]. This was the first experiment in which antennas and rectifiers were integrated to give what are now known as rectennas. The idea also proved to be feasible for Solar Power Satellites (SPS) in 1971. The next successful experiment on microwave power transmission was conducted at the Venus Site of JPL’s Goldstone Facility, where microwave power was transmitted over a one-mile distance to a rectenna array at a frequency of 2.388 GHz. The rectenna array was designed by W. Brown, which was later improved using the thin-film technology in 1977 [11]. After 1980, the MPT concept was pursued and extended internationally, mainly in Canada, Japan, and Europe. The Stationary High Altitude Relay Program (SHARP) was conceived in 1980 in Canada, as the first unmanned and remotely microwave-powered airplane for relaying telecommunication signals, surveillance, and monitoring services. The eighth-scale platform of SHARP shown in Figure 3.1(a), with a 4.5 m wingspan, was successfully tested at Canada’s Communications Research Centre (CRC) at an altitude of 150 m for 20 minutes, on September 17, 1987. The plane was remotely powered by a parabolic reflector antenna located on the ground at the frequency of 2.45 GHz, as shown in Figure 3.1(b). A dual-polarized rectenna array converted the microwave power to DC power, in order to lift and fly the 4.1 kg airplane [12], driving electric motors on the airplane for propulsion, powering the payload and controlling systems, and charging standby energy storage units. The thin-film rectenna used in SHARP was developed at the CRC. In 1992, Japan conducted the MIcrowave Lifted Airplane eXperiment (MILAX) using microwave power transmission technology. It was the first platform that utilized an electrically scanned phased array antenna to focus the antenna beam on the moving airplane, operating at a frequency of 2.411 GHz [13]. Japan was also engaged in the Solar Power Satellites (SPS), namely through the Microwave Ionosphere Nonlinear Interaction eXperiment (MINIX) in 1982 [14], and the International Space Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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(b)

Figure 3.1 The Stationary High Altitude Relay Platform (SHARP) unmanned plane; (a) the

aircraft, (b) a photo of the SHARP microwave-powered aircraft’s inaugural flight, with a view of the aircraft over the microwave transmitter. (Reproduced with permission of the Minister of Industry Canada 2015).

Year-Microwave Energy Transmission in Space (ISY-METS) in 1993 [15]. The latter was the first MPT-based example in space. Two other Japanese MPT-based projects are the Ground-to-Ground MPT program [16], with a 2304-element rectenna array at 2.45 GHz, and the SPRITZ program [17] conducted at Kyoto University with 1848 rectennas, which is one of the most advanced rectenna systems. During the 1990s to 2000s, the National Aeronautics and Space Administration (NASA) and Japanese researchers made significant advancements on Space Solar Power (SSP), by developing low-loss rectifiers for SSP applications. During the last decade, both SSP and MPT have continued to be topics of research interest. The most important projects were based on the inductive near field, and were conducted at the Massachusetts Institute of Technology and John Mankins’ Hawaii MPT demonstration [3].

3.3

Wireless Power Transmission Techniques The applications of wireless power transmission are quite wide, from remotely powering personal electronic devices to home appliances, radio-frequency identification (RFID) and bio-medical implantable devices, high-power long-range power transmissions, such as solar-power satellites, military, and industrial applications. From the electromagnetic and antenna points of view, basically there are two main techniques to transmit power wirelessly: near-field systems and far-field techniques. The former are based on either electric or magnetic induction, whereas the latter utilize microwave and laser transmissions. Essentially, efficiency, RF safety issues, and the frequency of operation are the key parameters to specify which of the aforementioned techniques are appropriate for a given application. For example, for distances up to a few meters and power requirements up to hundreds of watts, a near-field technique is preferred, because of the lesser RF exposures and higher efficiency, rather than the far-field technique.In particular, a

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near-field transmission operating at low frequency, such as 100 MHz and below, would perform better due to its capability of delivering higher equivalent plane-wave power densities than a far-field transmission [18]. In the following sections, the basic principles of these two methods are described.

3.3.1

Near-Field Wireless Power Delivery The near-field power transmission is used mainly for short- and mid-range power transmissions, e.g. distances from a few millimeters up to a few meters. Low-frequency (LF), high-frequency (HF), and ultra-high-frequency (UHF) RFID are well known applications, wherein the lower the frequency the shorter the range. The near-field technique is based on either induction or air ionization. The latter requires a high-intensity field in order to effectively transmit power between two conducting bodies, which is infeasible for practical applications. The famous example is lightning in nature, which is based on ionization of the air. In the former case, and from the electromagnetic point of view, there are two kinds of induction: electric and magnetic induction. Electric induction, also known as capacitive coupling, induces a change in voltage due to the varying electric field between two closely spaced conductors. Tesla’s famous experiment was based on this method, which is prone to cause electrocution. Thus, it is not a feasible approach for wireless power transmission due to the presence of high-intensity electric fields and the associated hazards to the human body and the surrounding environment. Magnetic induction, also known as inductive coupling, on the other hand, is relatively safer, and the induction is the result of a varying magnetic field between two adjacent conductors. Thus, due to the safety issues, near-field wireless power transmission systems are mostly based on the inductive or magnetic coupling method. The inductive coupling between two coils is best understood by considering the electric transformers that are used for up- or down-converting voltages. The basic block diagram is illustrated in Figure 3.2, where the power is transmitted by an alternating magnetic field in the primary coil to the secondary coil. The efficiency of power transmission depends on the mutual coupling factor between the coils, which is determined by the shape, distance between the coils, and enclosing material [19]. High-quality-factor coils [20], at both transmitting and receiving ends, as well as resonance coupled transformers, will increase the efficiency of the power transmission. In particular, the two coils interact very strongly under

Figure 3.2 Block diagram of a typical inductive coupling system [19].

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the resonance condition. Moreover, the efficiency can also be increased by exploiting multiple coils at the receiving end, where the user has access to hardware and its control [21].

3.3.2

Far-Field Wireless Power Delivery Far-field power transmission is used for long-range power delivery applications, for distances larger than the far-field range of the antennas. This form of power transmission is based on radiation. Therefore, there are two main techniques for far-field power delivery, using radio waves and light waves, known as microwave power transmission and laser power transmission, respectively. In 1919, Tesla demonstrated the concept of “true wireless” through the microwave power transmission technique [2]. Microwave power transmission is more efficient than laser power transmission owing to its higher efficiency of energy conversion and lesser attenuation in clouds. However, one needs a very-large-aperture antenna to focus the microwave beam, whereas a laser beam can be easily focused in a small area. The principles of energy transmission using a laser are very similar to those of microwave power transmission. In this chapter, the main focus is on the microwave power transmission, which can be used for both low- and high-power applications, such as low-power communication systems, wireless sensors, aerial vehicles, and space and military applications [18]. To date, due to safety issues, the far-field technique has not found widespread application for wireless powering of portable electronic devices. Instead, the nearfield technique, which is based on the magnetic coupling method, has been adopted more frequently. The microwave power transmission system consists of a transmitter and a receiver, wherein antennas play a key role at both ends. At the transmit end, the electromagnetic waves are directed through an antenna, which propagates in the medium of interest, e.g. free space. At the receive end, the EM waves will be received by an antenna or an array of antennas. They will then be converted to DC power through rectifiers. The combination of an antenna and a rectifier is known as a rectenna. Normally, the receivers also include matching networks and filters to match the antenna to the rectifiers and suppress higher-order harmonics, respectively. For long-distance ground-based wireless power transmission, the frequency range of 2 to 6 GHz is most suitable, due to there being significant atmospheric loss above 6 GHz and the large sizes of antenna apertures below 2 GHz. However, higher frequencies may be used for short distances and space or military applications. For example, frequencies of 35 and 94 GHz are commonly used for space solar power applications [22]. The opposite applies, on the other hand, when one considers the public safety and environmental effects of ground-based power transmission. In such cases, the use of high frequencies, beyond 6 GHz and into millimeter-wave frequencies, becomes desirable, to limit the propagation distance of the transmitted power. For communications systems, the Friis equation [23], based on far-field assumptions, is usually used to find the received power. When both antennas, at the transmit and receive ends, are uniformly excited, geometrically aligned, and 100% polarization matched, the received power, Pr , is expressed as

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Table 3.1. Collection efficiency for a given τ , with Gaussian aperture distributions [26] τ

0

0.5

1.0

1.5

2.0

2.5

3.0

Collection efficiency (%)

0

21

62

88

97

99

100

Pr =

Pt At Ar , λ2 R2

(3.1)

where R is the distance between the antennas with aperture sizes of At and Ar , at the transmit and receive ends, respectively. Also, λ is the wavelength of the operating frequency of the communication link. In wireless power transmission systems, the required received power is normally large, as opposed to the data communication link. Therefore, very large antennas are required in order to meet this condition. For an antenna with an aperture size of D, the far-field distance, R, is determined by the following inequality [24]: R>

2D2 . λ

(3.2)

As a practical example for solar power satellite applications, having a distance between the surface of the Earth and geosynchronous orbit of about 36,000 km, the antenna aperture size would be about 1,485 m at a frequency of 2.45 GHz. For such high-power solar applications, this will result in insufficient power being received according to the Friis equation. The wireless power link, however, has been accurately modelled, based on Goubau’s and Schwering’s method, by defining a new parameter, τ , pertinent to the collection efficiency [25], as expressed by √ At Ar . (3.3) τ= λR The value of τ changes from 0 to 3. The tabulated collection efficiency as a function of τ is listed in Table 3.1 [26], assuming Gaussian aperture distributions for the aperture antennas. For example, the τ = 3 case represents a collection efficiency of 100%.

3.4

Block Diagram of RF Wireless Power Transmission As mentioned in the previous sections, the applications of wireless power transmission are quite wide, from remotely powering hand-held electronic devices to implantable medical devices, and space and military applications. Herein, our main focus is on RF energy harvesting systems for a variety of applications, such as communications, monitoring, powering, diagnosis, and many more. The building blocks of an RF energy harvesting system are shown in Figure 3.3. The RF transmitter sends electromagnetic waves into space through a transmitting antenna. At the receiver, an antenna collects the EM waves and a rectifier converts the RF energy to DC power. In order to maximize the efficiency of the system, the antenna

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Figure 3.3 Building blocks of RF energy harvesting system.

is matched to the rectifier through a matching network. To effectively suppress the nonlinearity of the system and higher-order harmonics, a band-pass filter is also included in the receiver. The efficiency of the system mainly depends on that of the RF-to-DC conversion [27]. That is, ηRF−DC =

PRec , PRF

(3.4)

where PRec and PRF are the output DC power and incident RF power, respectively, as shown in Figure 3.3. The combination of the antenna, the rectifier, and the harmonic rejection filter is called a rectenna. One of the key components of RF energy harvesting systems is the radiating elements or antennas, which will be discussed in the next section. Another key component is the rectifier. Semiconductor diodes are mainly used for rectification. In particular, Schottky diodes are commonly employed as rectifiers. When one wants to obtain a high RF-to-DC conversion efficiency, the rectifiers play an essential role. Therefore, some design considerations should be taken into account. For example, diodes with low-loss and high-speed switching features are highly desired. In addition, zero-bias junction capacitance is preferred, which reduces the higher-order harmonics of the diode. Moreover, the rectifiers should handle low-power RF input signals, thus low-cut-off-voltage diodes are needed [28]. Having met all these criteria, when the receiving antenna is conjugately matched with the rectifier, the maximum rectification efficiency is realized. However, the input impedance of the diodes may vary as the input power changes, making the design of the matching a challenging task. This issue is addressed in [29].

3.5

Candidate Antennas The radiating elements or antennas are pivotal components of microwave power transmission systems. Depending on the application, omni-directional radiation patterns or directive beams are required. Simple and sophisticated antenna structures, such as dipoles and parabolic reflector antennas, are used to generate the aforementioned patterns, respectively. The typical geometries of these antennas are shown in Figure 3.4. In particular, the dipole antenna, due to its simplicity, was extensively used in the early stages of wireless power transmission. However, due to its resonant structure, it is a very narrowband antenna, which limits its applicability for multiband

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(a)

(b)

(c)

Figure 3.4 Typical geometry of (a) dipole antenna, (b) parabolic reflector antenna, and (c) horn

antenna.

and wideband systems. Reflector antennas, on the other hand, are complex in geometry, due to their curved surfaces, which makes them difficult to fabricate. They also require another feed antenna, as the illuminating source, at their focus in order to operate. Consequently, they are suitable candidates for high-gain and high-power applications, where other antennas become more expensive and less efficient. The main advantage of reflector antennas is in the principle of their operation. They are optically focusing devices, and have two focal points, one of which is located near the surface, as illustrated in Figure 3.4(b), and the other is at infinity. As such, they have a distinctive ability to generate focused beams in the far-field region, when the phase center location of the illuminating source is placed at the focal point. This property does not change with frequency or reflector size, and allows the generation of different gains, and operation at different frequencies. This is highly beneficial for long-range wireless power transmission applications, such as solar power satellites. In these applications, narrow beamwidth patterns, i.e. pencil-beam radiation patterns, are needed in order to focus the power within a desired area with minimum spillover loss. Hence, aperture distributions leading to high gain, narrow beamwidths, and extremely low sidelobe and backlobe levels are desired. Reflector antennas have another useful property. When the feed antenna is moved along the axis, away from the focal point, converging and diverging beams can be generated, which allows one to generate beams with increasing or decreasing power densities. For example, when the feed antenna is moved axially away from the reflector, its transmitted beam is focused at another axial point further away from the reflector. This can be a very useful property in microwave power transmission. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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The microwave power from an RF source can be delivered to a receiver further away from the source, but not at infinity. Since the reflector is a passive device, its frequency bandwidth and power handling capability are independent of the RF power source. It is therefore an ideal antenna for wideband and high-power microwave power transmission. The main drawback is the limitation of the beam scanning capability. For large beam scans, mechanical systems must be used to move the entire reflector system, which becomes heavy, complex, and very costly for large reflectors. In mobile applications this also places limitations on the response time of fast-moving systems. Mechanical systems have inertia and require more time and energy to move. On the other hand, reflector antennas, being passive devices, are more reliable and capable of handling large power levels, without the need for a change in design. Horn antennas are one of the most popular antenna candidates and are widely used in many applications, including reflector feeds, especially when dealing with high powers. The electromagnetic wave is confined within the horn structure, but travels in the air, making them more electrically efficient. Their simple geometry also makes them easy to fabricate. They are electromagnetic counterparts to acoustic horns and classified as medium-gain aperture antennas. They consist of open-ended waveguides flaring into a larger aperture to generate directive radiation patterns. There are different types of horn antennas depending on their shapes, such as pyramidal, conical, sectoral E-plane and H-plane, exponential, and corrugated horns. As an example, the geometry of a conical horn antenna is shown in Figure 3.4(c). In addition to the above antennas, phased array antennas are also extensively used in long-range applications. The phased array antennas are discrete versions of aperture antennas, i.e., reflector antennas, where the weighting factors of each element can be controlled electronically, thus offering extra degrees of freedom for beam forming and beam steering capabilities. The aforementioned requirements, in terms of gain, and sidelobe and backlobe levels, have still to be met; beyond which the extra factor of grating lobes needs to be taken into consideration. Grating lobes depend on the element spacing of the array structure. For example, for broadside radiation patterns, to avoid grating lobes, the element spacing should be less than one wavelength of the operating frequency. To control sidelobe levels, the elements of the array can be weighted according to the S-dB Taylor distribution, where S is the desired level of the sidelobes for a given application. As will be discussed later in this chapter, phased array antennas become attractive candidates when beam scanning is an important requirement, such as in massive MIMO applications. The selection of the array elements to form the array becomes more dependent on the system requirements and fabrication processes than on the antenna’s electrical performance. Generally, in RF energy harvesting applications, which are based on ambient radio-frequency sources, multiband and/or wideband antennas are much preferred. For wideband applications, spiral and helical antennas are excellent candidates, as they are theoretically classified as frequency-independent antennas. They are also known as traveling-wave antenna types, generating circularly polarized (CP) radiation patterns, which reduce the losses due to antenna misalignment at the transmit/receive ends and Faraday rotation. Typical geometries of these antennas are shown in Figure 3.5. It should be noted that the back radiation can be significantly suppressed Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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(a)

(b)

Figure 3.5 Typical geometries of antennas for wideband and circular polarization applications:

(a) spiral antenna and (b) helical antenna.

Figure 3.6 Geometry of circular microstrip patch antenna.

when the antennas are supported by a conducting ground plane, which reduces the spillover loss. However, their beamwidths are relatively wide. Thus, for beam focusing requirements, an array of such CP antennas may be utilized, which also provides added incentives, such as electronic beam steering, beam shaping, and adaptive nulling. Another type of antenna that is widely used in RF energy harvesting is the microstrip patch antenna, which in its original form is a planar structure. It has several advantages, such as low cost, low volume, light weight, conformal structure, and being compatible with integrated electronic devices. The patch is etched on a grounded dielectric slab and could be of any shape. The most popular shapes are circles and rectangles. As an example, a circular microstrip patch antenna is depicted in Figure 3.6. The technology of microstrip antennas has advanced rapidly in recent years, and most of its original limitations in shape and electrical performance have been eliminated. Currently, in a broader form a microstrip antenna is a finite-size metallization of a grounded dielectric, or any insulator, of planar or profiled shape, fed by a probe, a transmission line, or electromagnetic coupling to a nearby circuit, above or below the ground plane. The flexibility of its design has made the microstrip antenna a popular choice in communication and energy harvesting devices. In addition, because the feed network and the radiating patch can be etched, or metalized, concurrently on the substrate, arrays of microstrip antennas are simple to design, fabricate, and operate, especially in phased arrays, where the active devices can be embedded on the array surface. This possibility extends their applications into higher microwave and even millimeter-wave bands, Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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where other antennas become too small to be fabricated accurately with traditional and low-cost fabrication techniques. The resonant nature of microstrip antennas renders them inherently narrowband structures. However, there are techniques to make them work over wider frequency bands. To name a few, stacked patches, thick substrates, and slot-loaded patches can be used to enhance the bandwidth [30]. In the latter case, the slot can be placed on the ground plane, or on the patch itself. Some of the aforementioned methods are illustrated in Figure 3.7. The principle of broadbanding of microstrip antennas can be best explained in terms of coupled tuned circuits. Resonant antennas, such as microstrip patches and slots, are equivalent to an RLC circuit, and when used adjacent to each other can behave similarly to coupled tuned circuits. Thus, the broadbanding techniques of coupled tuned circuits can be used to make microstrip patch antennas wideband. However, since microstrip patch antennas are resonant structures, they operate due to the resonance of different modes, mostly the dominant mode, which is the TM11 mode for a circular patch antenna. For this reason, broadbanding of microstrip patch antennas is limited to about 2:1 frequency ratio, unless the feed system or the patch geometry is altered to prevent the excitation of higher-order modes. In this chapter, as a representative design example, single-layer slotted rectangular microstrip antennas, which are simple to fabricate are investigated. Since the energy harvesting can be over narrow or wide frequency bands, detailed design and performance studies are performed for two separate designs. The first design is intended for narrowband energy harvesting, and the second one is for wideband applications. In both designs the patch geometry is the same. Only the antenna dimensions are modified to make the design narrowband or wideband. Furthermore, to make the presented designs universal, the substrate permittivity is selected to be unity, so that the antenna sizes can be scaled to any frequency, without degradation of their performance. For this reason, the design (a)

(b)

Parasitic Patch

Patch

er2

Main Patch

er1 Ground

Slotted Ground

Probe (c) Patch

Aperture

Feed line

Figure 3.7 Examples of broadband microstrip patch antennas: (a) stacked patches, (b) a slotted

ground plane, and (c) aperture coupling methods. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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frequencies are selected to be at or around 1 GHz. This does not mean that the antennas designed here are intended for operation only at 1 GHz; rather, the selected frequency simplifies their scaling to other frequencies, simply by dividing the dimensions by the intended frequency, in GHz. For such designs, air, foam, or a honeycomb may be used as the antenna substrate, which also maximizes the antenna efficiency by eliminating lossy dielectrics. Even though the designs presented in this chapter are slotted patch antennas, the analysis of rectangular patch microstrip antennas is briefly reviewed in the following section, to show their operating principles and performance expectations.

3.5.1

Analysis of Rectangular Microstrip Patch Antennas The full-wave numerical methods, based on the method of moments, finite-element and finite-difference methods, are among the accurate methods to analyze microstrip patch antennas of any shape, with either finite or infinite ground plane sizes. However, they do not provide a scientific basis for understanding the operating principle of these antennas. This can be accomplished by using some approximate methods, which provide both physical insight and simple design procedures for microstrip patch antennas. The most well-known methods are the transmission-line and cavity models [24]. In this section, these two methods are briefly reviewed for rectangular microstrip patch antennas. The geometry of a rectangular microstrip patch antenna is shown in Figure 3.8, where L and W are the resonance length and width of the patch, respectively. The patch is etched on an infinite grounded dielectric slab with a relative permittivity εr and height h. According to the transmission-line model, which is essentially a one-dimensional model, there exist fringing fields at the edges of the patch, which make the patch electrically larger than its physical dimension. This directly affects the resonance frequency of the antenna, and hence should be taken into consideration. Owing to the fringing fields, the effective length of the patch will be the sum of the physical length of the patch, L, and twice the fringing length, L. That is, Leff = L + 2 L,

(3.5)

Figure 3.8 Geometry of a rectangular microstrip patch antenna.

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where the fringing length is given by [31] L (εreff + 0.3)(W/h + 0.264) = 0.412 , h (εreff − 0.258)(W/h + 0.8)

(3.6)

and the effective relative dielectric constant is denoted by εreff , which is a dispersive quantity. Its quasi-static value is commonly used as a good estimate to account for the fringing field, expressed by [32]

εreff =

  εr + 1 εr − 1 h −0.5 . + 1 + 10 2 2 w

(3.7)

For a thin substrate, where h is much smaller than the dielectric wavelength, the electric fields are nearly perpendicular to the patch. Therefore, only the transverse magnetic (TM) modes will be excited. According to the cavity model, the dominant mode is the TM10 mode, and the antenna becomes a half-wavelength rectangular patch. For this mode, the actual length of the patch will be determined by L=

c − 2 L, √ 2fr εreff

(3.8)

where c is the speed of light in free space, and L and εreff are given in equations (3.6) and (3.7), respectively. According to the cavity model, the rectangular microstrip patch antenna can be represented by a cavity, whose top and bottom walls are perfect electric conductors (PECs), and the four peripheral sides are perfect magnetic conductors (PMCs). On the PEC walls, the tangential electric fields are zero. Hence, there exist only equivalent electric currents, on the patch and ground plane. In contrast, on the PMC walls the tangential magnetic fields are zero, and there exist only non-zero electric fields that result in the equivalent magnetic currents. Therefore, the patch can be represented by four slots, at its edges, with four magnetic currents on their apertures. Using the image theory and equivalent principle, the radiated fields can be calculated from either the electric or the magnetic currents [32]. The electric current is unknown, but the magnetic currents at the patch edges can be calculated from the cavity modes, providing a simple method for computation of the radiated fields. For the dominant TM10 mode, only two of these slots contribute to the radiated fields. These radiating slots are along the resonance length of the patch, and their corresponding normalized far-field radiation components can be expressed by sin Y j(X+Y+Z) e−jkr e , Y r sin Y j(X+Y+Z) e−jkr e Eφ = −j sin φ cos X Y r

Eθ = j cos φ cos X

(3.9)

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where kLeff sin θ cos φ, 2 kw Y= sin θ sin φ, 2 kh Z= cos θ, 2 X=

(3.10)

and k is the free-space phase constant.

3.5.2

Conventional Microstrip Patch Antennas In most RF energy harvesting applications, and future massive MIMO applications, the antenna profile needs to be as small as possible in order to facilitate its integration with other electronic and radio-frequency components. From the radiation point of view, however, the antenna characteristics change as its structure becomes very compact and low profile. Thus, it is worth studying how the profile of a conventional microstrip antenna affects its overall performance in terms of gain and bandwidth. To demonstrate this, a rectangular microstrip antenna with a finite ground plane is investigated. The geometry of the antenna is depicted in Figure 3.9. The substrate is air with a nominal height of 9 mm. For an operation frequency near 1 GHz, the length and width of the patch are 131 mm and 142 mm, respectively, which have been numerically finalized. The patch is fed by a coaxial probe 23 mm away from its center along the resonant length. The impedance matching of the antenna, characterized by S11 , is shown in Figure 3.10, for different heights. As observed, the −10 dB impedance bandwidth widens as the antenna height increases, but for this conventional patch antenna the impedance bandwidth is narrow. The corresponding broadside gains are plotted in Figure 3.11. Near the resonance frequency of 998.5 MHz, the patch gain is about 9.4 dBi, and changes by dropping about 0.4 dB when the height increases from 9 mm to 13 mm. xs

w/2

f L

ys

L/2 + 23 mm

w

Figure 3.9 A rectangular microstrip patch antenna operating at 998.5 MHz, with L = 131 mm,

w = 142 mm, xs = 305 mm, ys = 228.6 mm, εr = 1, and a substrate thickness h = 9 mm. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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0

|S11| (dB)

–10

–20

–30 Antenna height = 5 mm Antenna height = 9 mm

–40

Antenna height = 13 mm

–50 0.95

1

0.975

1.025

1.05

Frequency (GHz) Figure 3.10 Magnitude of S11 of the rectangular microstrip antenna shown in Figure 3.9 for

different heights. 10

Peak Gain (dBi)

8

6

4

Antenna height = 5 mm Antenna height = 9 mm Antenna height = 13 mm

2

0 0.95

0.975

1

1.025

1.05

Frequency (GHz) Figure 3.11 Peak gain of the rectangular microstrip antenna shown in Figure 3.9 for different

heights.

Figure 3.12 Current distribution of the rectangular microstrip antenna shown in Figure 3.9, at f = 998.5 MHz and h = 9 mm. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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10

Gf at f = 90° Gq at f = 90°

Gain (dBi)

0

Gq at f = 90°

–10 –20 –30 –180

–120

–60

0 q (degrees)

60

120

180

Figure 3.13 Radiation patterns at φ = 0◦ , 90◦ of the rectangular microstrip antenna shown in

Figure 3.9 at f = 998.5 MHz and h = 9 mm. 0

|S11| (dB)

–10

–20 –30

tan d = 0 tan d = 0.0022 tan d = 0.02

–40 –50 0.95

0.975

1

1.025

1.05

Frequency (GHz) Figure 3.14 Magnitude of S11 of the rectangular microstrip antenna shown in Figure 3.9, for

different loss tangents, when h = 9 mm.

For the case with h = 9 mm, the surface current distribution on the patch is shown in Figure 3.12, at the resonance frequency of 998.5 MHz. This shows that the antenna is linearly polarized along its resonant length. For the sake of completeness, the corresponding radiation patterns of the antenna are illustrated in Figure 3.13, at the frequency of 998.5 MHz, when h = 9 mm. The antenna has broadside radiation patterns with a peak at the boresight angle of θ = 0◦ . The boresight gain is about 9 dBi and the peak cross-polarization component, in the φ = 90◦ plane, is below −22 dB. To complete the study, the effect of the dielectric loss of the substrate, or loss tangent, on the impedance bandwidth and efficiency of the antenna is also studied. Three cases are investigated, with loss tangent values of zero, 0.02, and 0.0022. The results are shown in Figures 3.14 and 3.15. It can be seen that the −10 dB impedance bandwidth of the antenna, for the selected range of the substrate loss, is not very sensitive to the dielectric loss. However, the antenna efficiency deteriorates as the dielectric loss increases, as expected. The antenna efficiency drops from 100% for a lossless substrate Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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100

Efficiency (%)

80

60

40

tan d = 0 tan d = 0.0022 tan d = 0.02

20

0 0.95

0.975

1

1.025

1.05

Frequency (GHz) Figure 3.15 Radiation efficiencies of the rectangular microstrip antenna shown in Figure 3.9, for different loss tangents, when h = 9 mm.

to near 80%, when the dielectric loss becomes considerably larger with a loss tangent of 0.02. The latter results for the efficiency show the significance of the dielectric material and its electrical loss property on the antenna transmission efficiency. While this may be accommodated in signal transmission, it will be a serious deficiency in power transmission, and should be considered in the antenna designs for energy harvesting. In the proposed designs, the substrate permittivity is assumed to be unity, to eliminate this loss.

3.6

Universal Design Examples: Slotted Microstrip Patch Antennas In practice, the bandwidth of energy harvesting and communication systems could be of different sizes. It could be over a narrowband, multiband, or wideband range. The narrowband and wideband designs are the extreme cases, and the multiband one can in principle be obtained by detuning the wideband case. For this reason, in the following section two designs are provided and investigated for impedance and radiation properties. Both designs are based on the slotted patch configuration, which even for the wideband case results in a single-layer configuration. The single-layer geometry facilitates its fabrication or array applications, and is suitable for applications in handheld or other small communication devices. Because of their superior performance, they are also used in other communication devices, and will be a good candidate for antenna arrays for massive MIMO applications. As indicated earlier, the relative permittivity of the antenna substrate will be selected as unity, to eliminate the substrate loss, and allow antenna size scaling to other frequencies.

3.6.1

Design I: Narrowband and Slotted-Microstrip Antenna (1% bandwidth) The geometry of a slotted microstrip patch antenna is shown in Figure 3.16. It is essentially a rectangular microstrip patch with a resonant slot embedded on its surface. Since the length of a resonant slot is longer than the width of the patch, the slot is bent to fit on

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Table 3.2. Dimensions of the narrowband antenna as shown in Figure 3.16 (all values are in mm) L

w

d1

d2

d3

ul

uw

a1

a2

xs

ys

h

135

150

44.75

10

23

97

40.5

39.3

85

305

228.6

9

(a) w d2 ys f

ul

L

uw

d1 a1

d3 a2 y

xs x (b)

Patch Antenna

Ground Plane h

h

(c)

Figure 3.16 (a) Top-view geometry and (b) side-view of a U-slot microstrip patch antenna with εr = 1, and (c) a picture of the experimental prototype. The patch is placed on top of the ground plane at distances (h) of 9 mm and 27 mm for a narrowband and wideband antenna, respectively.

the patch surface. The shape of the bent slot is not important for impedance bandwidth broadening, and can be made U-shape [33–37], circular [38], trapezoidal [39–45] or other shapes [46–49]. Table 3.2 shows the dimensional parameters of the antenna, which was designed for operation at 980 MHz, on a substrate with a relative permittivity of unity. Thus, its slotted patch is suspended over the ground plane, or placed on a foam or honeycomb substrate, and does not require a solid substrate, making it simple and cheap to fabricate, and allowing size scaling for other frequencies. Figures 3.17 and 3.18 show plots of its S11 and VSWR, as a function of the feed probe diameter, which can be used to match the Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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0

|S11| (dB)

–10 –20 rin probe = 2.5 mm

–30

rin probe = 4.0 mm –40 –50

rin probe = 4.5 mm

0.96

0.98

1

1.02

1.04

1.06

Frequency (GHz) Figure 3.17 Magnitude of S11 of the narrowband antenna shown in Figure 3.16 with

corresponding dimensions given in Table 3.2, for different radii of the feed probe. 6

rin probe = 2.5 mm rin probe = 4.0 mm

5

VSWR

rin probe = 4.5 mm 4 3 2 1

0.96

0.98

1

1.02

1.04

1.06

Frequency (GHz) Figure 3.18 VSWR of the narrowband antenna shown in Figure 3.16 with corresponding dimensions given in Table 3.2, for different radii of the feed probe.

input terminal of the antenna to a 50  transmission line. The antenna is of low profile and its −10 dB return loss bandwidth is about 1%, which is narrowband. The current distribution on the patch is shown on Figure 3.19, which shows linear polarization. Its radiation patterns are shown in Figure 3.20, indicating a peak gain of about 10 dBi, and a peak cross polarization of less than −20 dB, in the φ = 90◦ plane. It is a simple antenna to fabricate and its narrow operating band facilitates its isolation from other sources, or communication bands.

3.6.2

Design II: Wideband Slotted-Microstrip Antenna (45% bandwidth) The geometry of this design is the same as that in Figure 3.16, but its dimensional parameters are changed to increase its frequency bandwidth to 45%, which is significant. Its dimensional parameters are shown in Table 3.3. The corresponding S11 and VSRW are shown in Figures 3.21 and 3.22, again as a function of the feed probe

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Table 3.3. Dimensions of the wideband antenna as shown in Figure 3.16 (all values are in mm) L

w

d1

d2

d3

ul

uw

a1

a2

xs

ys

h

130

220

75

10

25

82

50

42.5

87.5

305

305

27

Figure 3.19 Current distribution of the narrowband antenna shown in Figure 3.16 with corresponding dimensions given in Table 3.2, at the frequency of 980 MHz, when the probe radius is 4 mm.

10

Gf at f = 90° Gq at f = 90°

Gain (dBi)

0

Gq at f = 90°

–10 –20 –30 –180

–120

–60

0

60

120

180

q (degrees) Figure 3.20 Radiation patterns at φ = 0◦ and 90◦ at the frequency of 980 MHz of the narrowband

antenna shown in Figure 3.16 with corresponding dimensions given in Table 3.2, when the probe radius is 4 mm. The cross polarization is shown by the pale shaded line.

diameter. The solid lines correspond to the highest achieved bandwidth. The current distribution is shown in Figure 3.23, again indicating a linearly polarized antenna. A sample of the radiation patterns is shown in Figure 3.24. The peak gain is about 9 dBi, and its cross polarization is less than −20 dB. As in the previous case, the substrate permittivity is selected to be unity, so that its slotted patch is suspended over the ground plane, and it does not require a solid substrate, making it simple and cheap to fabricate. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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0

|S11| (dB)

–10

–20

–30

rin probe = 2.5 mm

–40

rin probe = 4.5 mm

rin probe = 4.0 mm

–50 0.8

0.9

1

1.1

1.2

1.3

Frequency (GHz) Figure 3.21 Magnitude of S11 of the wideband antenna shown in Figure 3.16 with corresponding

dimensions given in Table 3.3, for different radii of the feed probe. 6

rin probe = 2.5 mm rin probe = 4.0 mm

5

VSWR

rin probe = 4.5 mm 4 3 2 1 0.8

0.9

1

1.1

1.2

1.3

Frequency (GHz) Figure 3.22 VSWR of the wideband antenna shown in Figure 3.16 with corresponding dimensions given in Table 3.3, for different radii of the feed probe.

Figure 3.23 Current distribution of the wideband antenna shown in Figure 3.16 with corresponding dimensions given in Table 3.3, at the frequency of 700 MHz, when the probe radius is 4 mm.

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10 Gf at f = 90° Gq at f = 0°

Gain (dBi)

0

Gq at f = 90°

–10 –20 –30 –180

–120

–60

0 60 q (degrees)

120

180

Figure 3.24 Radiation patterns at φ = 0◦ and 90◦ at the frequency of 700 MHz of the wideband

antenna shown in Figure 3.16 with corresponding dimensions given in Table 3.3, when the probe radius is 4 mm. 0

|S11| (dB)

–10 –20 –30

Patch width = 21 cm Patch width = 22 cm Patch width = 23 cm

–40 –50

0.8

0.9

1

1.1

1.2

1.3

Frequency (GHz) Figure 3.25 Magnitude of S11 of the microstrip antenna shown in Figure 3.16 with corresponding

dimensions given in Table 3.3, for different patch widths. 10

Peak Gain (dBi)

8 6 4

Patch width = 21 cm Patch width = 22 cm Patch width = 23 cm

2 0

0.8

0.9

1

1.1

1.2

1.3

Frequency (GHz) Figure 3.26 Peak gain of the microstrip antenna shown in Figure 3.16 with corresponding dimensions given in Table 3.3, for different patch widths.

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It is worth studying how the width of the patch affects the frequency bandwidth and gain of the wideband microstrip antenna under investigation. The results are shown in Figures 3.25 and 3.26. It can be observed that the −10 dB impedance bandwidth widens as the width of the patch increases. The peak gain on the axis, i.e., at θ = 0◦ , is almost unchanged up to 1.1 GHz, and drops drastically thereafter.

3.7

Wideband Diversity Antennas

3.7.1

Introduction It has long been known that the capacity of a communication channel is linearly proportional to the bandwidth, meaning that higher data rates are achievable with a wider bandwidth. As mentioned above, a wideband antenna can be designed to cover a large frequency band or be detuned to cover multiple smaller frequency bands. Another important concept in improving wireless communication is the antenna diversity. The goal in diversity schemes is to introduce new channels in an existing communication link to increase the capacity [50, 51]. These schemes include spatial diversity, radiation pattern diversity, and polarization diversity. In spatial diversity, multiple antennas cover several locations [52]. With adequate separation between antennas, the signals received by each antenna will be uncorrelated (or partially correlated) to others, therefore increasing the probability of receiving at least one signal that has not experienced deep fading. This method is widely used in base station cell towers. In radiation pattern diversity, several co-located antennas cover different angular directions for reception and/or transmission. Each antenna therefore should have a directive pattern, which covers a specific portion of the angular space. As for the polarization diversity, a single dual-polarized antenna provides two independent channels that can work simultaneously, each using one of the antenna polarizations. In this scheme the isolation between the channels is governed by the level of antenna cross polarization, which becomes a critical parameter of the antenna diversity. Diversity schemes implemented in base stations lead to improvement in the reliability of a communication system by reducing the co-channel interference, fading, and biterror rate. In addition, the same schemes can be deployed in mobile handheld devices, leading to lower required transmission power (for a given level of reliability) and therefore lower levels of interference (with other devices) and longer battery life [52]. These desirable features have resulted in diversity schemes to be studied as a component of the newly emerging wireless-powered communication networks too [53]. For example, the performance of such a network with a multi-antenna access point (AP), delivering information and energy to single antenna users, was recently studied in [54]. It is also possible to use omni-directional antennas, as opposed to directional elements such as the U-slot patch, to achieve pattern diversity. This allows more compact designs, which are suitable for mobile handheld devices. Various wideband diversity antennas of this type have been designed in the past decade, with most emphasis on planar twoelement configurations [55–61]. The antennas are placed as close as possible, which makes it difficult to maintain high levels of isolation. This issue is usually addressed

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by shaping the ground plane [55–58], or using neutralization lines [59, 60]. To further reduce the size of a two-antenna system, in [61], a single wideband element is fed from two sides at 90◦ angle. In this technique, which was applied to a disk and a square monopole antenna, the radiation pattern is either directional or omni-directional, for out-of-phase and in-phase excitations, respectively. These antennas are mainly designed for ultra-wideband (UWB) applications, covering the frequency band 3.1 GHz to 10.6 GHz. Another class of antennas used in diversity schemes is the tapered-slot antennas. Also known as Vivaldi antennas, tapered-slot antennas have been studied extensively in the literature and are known for their large bandwidths with directive radiation patterns. Although they are not in general low-profile antennas, their excellent characteristics, simple geometry, and scalability to a wide range of frequencies have made them attractive for many applications [62]. A compact dual-polarized UWB antenna, embedded in dielectric, was designed in [63], where the polarization diversity was achieved by placing two Vivaldi elements orthogonally. Tapered-slot monopoles have also been studied recently. In [64], a wideband Vivaldi monopole operating from 620 MHz to 2.6 GHz is designed to cover the LTE, GSM, and UMTS bands simultaneously. The application of the same antenna in an angular periodic configuration is also studied in [65], where a simple method for beam steering with only one or two active antennas has been presented. In another configuration, a combination of monopole and slot antennas was used on the existing ground plane of a small 50 mm × 80 mm, typical PC wireless card, to design a wideband antenna, without the need for a separate antenna space on the card [66]. Locating the antenna at two orthogonal locations on the card provided a compact dual-polarization-pattern diversity antenna.

3.7.2

Pattern Diversity Implementation To implement pattern diversity, multiple antenna elements are placed in a specific configuration, usually sharing a common ground plane. For a planar structure, a simple configuration may be a conventional planar array of low-profile antenna elements such as the wideband U-slot patch antenna introduced in Section 3.6.2. For instance, a twoelement configuration is shown in Figure 3.27. Assuming the two antennas are excited z

x

y

Figure 3.27 A two-element array of U-slot patches; the antenna polarization is along the y-axis.

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Gain (dBl)

10 0 –10 –20 –180 –135 –95 –45 0 45 90 135 180 q (degrees) (a) Gain Patterns of a single U-slot patch

10 Gain (dBi)

Gain (dBi)

10 0 –10

–180 –135 –95 –45 0 45 90 135 180 q (degrees) V1 = V2, f = 600 MHz

–180 –135 –95 –45 0 45 90 135 180 q (degrees) V1 = –V2, f = 600 MHz

10

10 Gain (dBi)

Gain (dBi)

–10 –20

–20

0 –10 –20

0 –10 –20

–180 –135 –95 –45 0 45 90 135 180 q (degrees) V1 = V2, f = 800 MHz

–180 –135 –95 –45 0 45 90 135 180 q (degrees) V1 = –V2, f = 800 MHz

10

10 Gain (dBi)

Gain (dBi)

0

0 –10 –20

0 –10 –20

–180 –135 –95 –45 0 45 90 135 180 q (degrees) V1 = V2, f = 1000 MHz

–180 –135 –95 –45 0 45 90 135 180 q (degrees) V1 = –V2, f = 1000 MHz

(b) Array of two U-slot patches Ey (x–z plane) Ey (y–z plane) Ex (x–z plane) Figure 3.28 Gain patterns of (a) a single U-slot patch at 600 MHz and (b) the gain patterns of the two-element array of Figure 3.27, for in-phase and out-of-phase excitations. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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by two voltages V1 and V2 , if they are fed in-phase (V1 = V2 ), their radiated fields add up in the broadside direction, i.e. along the z-axis, therefore the total radiated field would still be in the broadside direction. Out-of-phase excitation of the patches (V1 = −V2 ), on the other hand, results in cancellation of the fields exactly along the z-axis. The total radiation pattern in this case has a null along the broadside direction. This is demonstrated in Figure 3.28. In Figure 3.28(a), the gain patterns of a single U-slot patch at 600 MHz are given. Choosing a separation of 0.5 wavelength at 600 MHz, the radiation patterns of the array in Figure 3.27 are calculated as shown in Figure 3.28(b), for in-phase and out-of-phase excitations. Assuming similar radiation patterns for the U-slot patch at higher frequencies, the total radiation patterns of the array at 800 and 1000 MHz are also shown. Because of the location of the U-slot on the patch, the polarization of this antenna is along the narrow side of the patch, i.e., the y-axis in Figure 3.27. If dual polarization is required, four-element arrays of U-slot patches, similar to those in Figure 3.29(a) and (b), can be used. These sub-arrays can also be used to form larger arrays, as shown in Figure 3.29(c). Since the U-slot patch is geometrically larger than conventional microstrip patches, in array formations lesser array elements will be required in order to achieve the required array gains, which can be an advantage. In scanning active arrays, the lesser array element means lesser phase shifters and power dividers, and thus simpler and cheaper arrays. However, the larger inter-element spacing (a)

(b)

z

z

y

x

y

x z

(c)

x

y

Figure 3.29 Arrays of U-slot patches for dual polarization: (a) a four-element array, (b) a compact four-element array, and (c) a 10 × 10 array of U-slot patches, which is a 5 × 5 array of sub-array (b).

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(a)

(b)

z

y

x (c)

x

113

z

y

Figure 3.30 Arrays of square microstrip patch antennas for dual polarization: (a) front view of a four-element array and (b) three-dimensional (3D) view, and (c) a 10 × 10 array of square patches, which is a 5 × 5 array of sub-array (b).

of U-slot patches limits the scan range of the array, due to the appearance of grating lobes at large scan angles, which reduces the array gain and causes deterioration of its radiation patterns. In such cases, smaller conventional patch array may be used, as shown in Figure 3.30, using square patches. Electrically, there is an important difference between large single polarized patches, such as the U-slot patch, and small square patches. By feeding the square patch along two orthogonal axes, shown as two dots on Figure 3.30, one can generate dual polarization from a single patch. Circular polarization is also possible with both array types. However, in using the U-slot type patches one must use sub-arrays, such as those in Figures 3.29(a) and (b), to generate circular polarization, as each element is linearly polarized. The square patch elements of Figure 3.30, on the other hand, can be fed along two orthogonal axes at phase quadrature to generate circular polarization from each array element. In this case, there is an additional difference between the two designs. Using linearly polarized elements to generate circular polarization is effective only in large arrays. In smaller arrays, a penalty is paid in terms of the array gain, which could be as much as 2 dB, depending on the array size. Microstrip patch antennas are of low profile and can be integrated easily with electronics. Hence, they are good candidates for applications in communications and energy harvesting. However, they are also resonant structures and have bandwidth Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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limitations. For bandwidths in excess of 50%, other antenna configurations should be considered. An example of a wideband antenna, consisting of four tapered-slot monopole elements, is presented for polarization and pattern diversity.

3.8

Design III: Wideband Dual-Diversity Antenna In Section 3.6, a universal slotted-patch antenna was introduced and designed for both narrow and wide impedance bandwidth applications. Its polarization and pattern diversities were also presented and discussed in Section 3.7. It is a low-cost planar antenna, with a substrate permittivity of unity and can be scaled to any frequency band. However, because it was based on a resonant patch configuration, its wide impedance bandwidth was limited to 45%. Beyond that, the higher-order modes of the patch become excited and the antenna performance deteriorates. In Section 3.7, we discussed also other wideband antennas, such as Vivaldi antennas, which are capable of dual diversity as well, i.e., both polarization and pattern diversity. However, at higher frequencies, beyond the Ka-band, they become too lossy and inefficient. For these reasons, in this section we introduce a third universal design, which has both polarization and pattern diversity and can be designed for full UWB band operation. However, since the objective of this chapter is not the design of UWB antennas, results are provided only for an octave frequency band, centered at 1 GHz. Again, the design is selected such that the antenna dimensions may be scaled easily to any other frequency band, simply by dividing the antenna dimensions by the frequency of operation, in GHz. Another important feature of this design is that its geometry is compatible with fabrication using micromachining techniques, and thus it can be fabricated easily, even at millimeterwave bands, including the upper 5G communication bands. Below is a description of the antenna, which is based on tapered-slot antennas. A typical tapered-slot antenna is shown in Figure 3.31(a). The smooth transition from a narrow slot line into free space, using such a geometry, ensures good impedance matching over a wide frequency band. The monopole version of the same geometry is (a)

(b)

(c)

Figure 3.31 Design of a dual-diversity antenna based on a tapered-slot monopole.

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(a)

(b) Etotal

Etotal

Z k1

115

E1

E2

k2

V V In-phase excitation

Y

k1

E1

E2

k2

V –V Out-of-phase excitation

Figure 3.32 The two operating modes of the diversity antenna of Figure 3.31(c).

depicted in Figure 3.31(b), where the lower half is replaced with a (large enough) ground plane. The advantage of this monopole over its dipole counterpart is the increased gain, as the radiation is directed into the upper half-plane. Also, it can be fed with a simple coaxial feed, since the monopole is an unbalanced geometry and does not require a balun. With this monopole, a novel geometry for a pattern diversity antenna can be formed as shown in Figure 3.31(c), where two monopoles are placed back-to-back, at a 45◦ angle with respect to the z-axis. The operating principle of this two-element system is demonstrated in Figure 3.32. With in-phase-excitation of the ports, as shown in Figure 3.32(a), the y-components of the electric fields cancel out, leaving a null along the z-axis. Out-of-phase excitation of the ports, on the other hand, results in constructive interference of the y-components of the electric fields along the z-axis. The radiation pattern in this case has its peak along the z-axis with a linear polarization parallel to the y-axis. To add polarization diversity then, another pair of elements must be crossed with the initial two elements, as shown in Figure 3.33. The ground planes of the four elements are connected to form a horn-shaped common ground. As indicated in the side view, each element is fed by a coaxial port. A photograph of the prototype antenna is shown in Figure 3.33. Because of its large size, to fabricate the ground cavity, the side plates were cut from a 2 mm thick aluminum sheet, and inter-connected mechanically with screws. The four SMA feeds were placed at the edges of the bottom plate, at the middle of each side plate. The four elements were cut from copper tape and placed on two acrylic sheets. It should be noted, however, that this type of antenna does not require any dielectric and can be fabricated with thick metal sheets as antenna elements. The acrylic sheets were therefore used only for supporting the elements, which were made of copper tapes. Thus, the antenna can be scaled to other frequencies by dividing its dimensions by the frequency of operation. For instance, at 60 GHz, which is one of the 5G frequency bands, the antenna dimensions reduce to below 0.8 cm × 0.33 cm, and it can be fabricated by machining, or 3D printing. As will be shown below, the configuration is a dual-diversity antenna, with both polarization and pattern diversity. It should also be noted that, in array forms, feed networks can be etched on the array ground plane, and can be connected to the elements through vias, which greatly simplifies the array fabrication. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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(a)

(b)

Z

Z

X

Y

50 c

m

m 0c

X

Y

5

#3

#4

20 cm #2

15 cm

#1 port 1 3D view

port 3 Side view

(c)

Antenna prototype Figure 3.33 Wideband polarization and pattern diversity antenna with four tapered slot monopoles: (a) 3D view, (b) side view, and (c) picture of the fabricated prototype.

The scattering parameters of the antenna are given in Figure 3.34. Owing to the geometric symmetry, only three S-parameters are shown. The first plot in Figure 3.34(a) shows the input reflection coefficient of each port, when all other ports are terminated by matched loads. The second plot in Figure 3.34(b) shows the coupling between the two adjacent ports, while the coupling between the two facing ports is given in Figure 3.34(c). There is good agreement between the simulated and measured results. It is desirable that all of these values are small, to ensure that the antenna radiates power efficiently. Another figure of merit, when analyzing a diversity antenna, is the envelope correlation coefficient, ρ, which is a measure of the orthogonality of the two patterns and is given by ρ = 



F2 (θ, φ)]d|2 4π [F1 (θ, φ) • 2 2 4π |F1 (θ, φ)| d 4π |F2 (θ, φ)| |

, d

(3.11)

where F1 and F2 are the complex radiation patterns of antennas 1 and 2 and • denotes a Hermitian inner product. The value of ρ can change from 0 to 1, where 0 denotes Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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(a) 0

S11 (dB)

simulated measured –10

–20

–30 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Frequency (GHz) (b) 0

S12 (dB)

simulated measured –10

–20

–30 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Frequency (GHz) (c) 0

S13 (dB)

simulated measured –10

–20

–30 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Frequency (GHz) Figure 3.34 The scattering parameters of the antenna shown in Figure 3.33: (a) the reflection coefficient, (b) coupling between two adjacent ports, and (c) coupling between two facing ports.

completely orthogonal patterns and 1 denotes two identical patterns. For uniformly distributed channels and lossless antennas, this formula can be modified [66] to give   ∗ S S12 + S∗ S22 2 11 21 ρ=     , 1 − |S11 |2 + |S21 |2 1 − |S22 |2 + |S12 |2

(3.12)

which is expressed in terms of the input S-parameters and therefore is easier to calculate and measure. This relationship and the input S-parameters in Figure 3.34 can be used to Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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(a) 100 simulated measured

–1

|r12|

10

10–2 10–3 10–4 0.4

0.5

0.6

0.7 0.8 0.9 1 Frequency (GHz)

1.1

1.2

(b) 100 simulated measured

|r13|

10–1 10–2 10–3 10–4 0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Frequency (GHz) Figure 3.35 Envelope correlation coefficients of the antenna shown in Figure 3.33: (a) two adjacent ports and (b) two facing ports.

(a)

(b) z

z

Theta

x

Theta

y dB(Dir Theta)

Phi

1.2000e+001 1.0071e+001 8.1429e+000 6.2143e+000 4.2857e+000 2.3571e+000 4.2857e+001 –1.5000e+000 –3.4286e+000 –5.3571e+000 –7.2857e+000 –9.2143e+000 –1.1143e+001 –1.3071e+001 –1.5000e+001

V1 = V3 = 1; V2 = V4 = 0;

(c) z Theta

x

Phi

V1 = –V3 = 1; V2 = V4 = 0;

y

y

Phi

x

V1 = V3 = 0; V2 = V4 = 1;

(d) z Theta

x

Phi

y

V1 = V3 = 0; V2 = –V4 = 1;

Figure 3.36 The radiation patterns of the antenna in Figure 3.33 at 800 MHz, for different excitations. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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f = 550 MHz

f = 600 MHz

f = 650 MHz

f = 700 MHz Curve Info Ex (x–z plane) Ex (y–z plane) Ey (x–z plane) Ey (y–z plane)

Curve Info Eq (x–z plane) Eq (y–z plane) Ef (x–z plane) Ef (y–z plane)

Figure 3.37 The normalized patterns of the antenna shown in Figure 3.33, for in-phase (right column) and out-of-phase (left column) excitations of the pair in the x–z plane, in the frequency range 550–700 MHz.

calculate the envelope correlations coefficients for the two adjacent elements and two facing elements as shown in Figure 3.35. As mentioned earlier, the radiation patterns of the antenna depend on the phase difference between the excitations of the ports. For in-phase excitation of the pair in the x–z plane, as shown in Figure 3.36(a), two major lobes form in the x–z plane. Similarly, Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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f = 750 MHz

f = 800 MHz

f = 850 MHz

f = 900 MHz Curve Info Ex (x–z plane) Ex (y–z plane) Ey (x–z plane) Ey (y–z plane)

Curve Info Eq (x–z plane) Eq (y–z plane) Ef (x–z plane) Ef (y–z plane)

Figure 3.38 The normalized patterns of the antenna shown in Figure 3.33, for in-phase (right column) and out-of-phase (left column) excitations of the pair in the x–z plane, in the frequency range 750–900 MHz.

for the pair in the y–z plane, the in-phase excitation of the ports results in the formation of two lobes in the y–z plane. This is depicted in Figure 3.36(b). On feeding two facing elements in out-of-phase manner, the fields along the z-axis add up, resulting in a directive pattern. This pattern is linearly polarized along the elements, i.e., for the pair in the x–z plane, the field is x-polarized; and for the pair in the y–z plane, the radiated field is y-polarized. These two cases are shown in Figures Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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f = 950 MHz

f = 1000 MHz

f = 1050 MHz

f = 1100 MHz Curve Info Ex (x–z plane) Ex (y–z plane) Ey (x–z plane) Ey (y–z plane)

Curve Info Eq (x–z plane) Eq (y–z plane) Ef (x–z plane) Ef (y–z plane)

Figure 3.39 The normalized patterns of the antenna shown in Figure 3.33, for in-phase (right column) and out-of-phase (left column) excitations of the pair in the x–z plane, in the frequency range 950–1100 MHz.

3.36(c) and (d), respectively. For completeness, the normalized radiation patterns of the antenna, over its designed frequency band, are shown in Figures 3.37–3.39. The left side shows the out-of-phase patterns with axial high gains, and the right side shows the same for in-phase excitations. They clearly show the pattern and polarization diversity of the antenna. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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Peak Gain (dBi)

122

14 12 10 8 6 4 2 0 –2 –4 0.5

0.6

0.7

1.2

1.1

1 0.9 0.8 Frequency (GHz)

Figure 3.40 Peak gain of the diversity antenna of Figure 3.33 versus frequency, for the pair in the x–z plane. Solid line, out-of-phase excitation; dashed line, in-phase excitation (x–z plane); dot–dashed line, in-phase excitation (y–z plane).

3 dB Beamwidth (degrees)

90 x–z plane y–z plane

80 70 60 50 40 30 20 10 0 0.5

0.6

0.7

0.8 0.9 Frequency (GHz)

1

1.1

1.2

Figure 3.41 The 3 dB beamwidths of the diversity antenna of Figure 3.33 versus frequency, for out-of-phase excitation of the pair in the x–z plane.

f = 550 MHz

f = 800 MHz

f = 1100 MHz

Curve Info E LHCP (x–z plane) E LHCP (y–z plane) E RHCP (x–z plane) E RHCP (y–z plane)

Figure 3.42 The normalized patterns of the antenna shown in Figure 3.33, when ports are excited as V1 = 1, V2 = 1ej90 , V3 = −1, and V4 = 1ej270 , leading to CP operation.

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The variation of the peak gain with frequency is shown in Figure 3.40. It can be seen that the gain is stable up to 1.1 GHz. For the case of out-of-phase feeding, the 3 dB beamwidth of the pattern as a function of frequency is given in Figure 3.41. The operating bandwidth of the antenna is therefore from 520 MHz to 1.1 GHz, which is an octave band, and can be increased, if desired, by modifying the antenna dimensions. It is worth mentioning that in addition to the aforementioned linear polarizations, it is also possible to create circular polarization (CP) with this geometry. For this case, a phase progression of 2π from element 1 to element 4 is required. The trend of this progression determines the sense of rotation (whether it is right-handed or left-handed CP). For example, a positive phase progression results in a left-handed CP operation. This is demonstrated in Figure 3.42, where the normalized radiation patterns at different frequencies are shown.

3.9

Antennas for Massive-MIMO Applications So far the antenna designs presented in this chapter were intended for applications involving energy harvesting. However, the designs presented are equally applicable for signal communications, and the difference in requirements is quite small. For instance, for energy harvesting the antenna efficiency is the most important parameter, while the frequency bandwidth may not be a critical parameter, since microwave power transmission is most likely to occur over a narrow frequency band. The bandwidth, however, is an important parameter for signal transmission. To make the proposed designs useful for both applications, the sources of resistive losses are minimized. For this reason, dielectric materials such as microwave substrates are excluded from the designs. The same approach may also be used in massive-MIMO designs. Thus, in this section we review the antenna designs from the point of view of their radiation performance, regardless of their intended application for power or signal transmission. To address the staggering increase of wireless signal traffic, massive MIMO considers the use of multiple antennas at base stations (BSs), the number of which can increase by orders of magnitude. The antenna configurations, however, must be cheap while providing the most reliable operation possible. Planar arrays provide promising designs. An example is shown in Figure 3.43, which is a 10 × 10 array of microstrip patches. z

x

y

Figure 3.43 A 10 × 10 planar array of microstrip antenna elements.

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0

n=1 n=2 n=4 n=6 n=8

Normalized Gain (dB)

–2

–4

–6

–8

–10 –90

–60

–30

0 30 q (degrees)

60

90

Figure 3.44 Variation of microstrip array beamwidths with number of array elements, along

each axis.

It has a simple geometry and is easy to fabricate. The beamwidth of such an array is shown in Figure 3.44, for different array elements. It is clear that the radiation pattern beamwidth decreases progressively on increasing the array elements. Thus, the coverage zone of the array decreases rapidly. For optimum coverage, thus, the array beam must be scanned to cover the entire coverage zone. In addition, to benefit from the advantages of massive MIMO, all array beams must be available concurrently, which is seldom the case in other phased array applications. Unfortunately, even neglecting the concurrent needs for all array beams, there are consequences for wide-angle scans of large array beams, two of which are scan gain loss and beamforming network complexity. For the 10 × 10 microstrip array, neglecting the mutual coupling, the reduction of the array gain along one of its axis is shown in Figure 3.45, which is due to the reduction of its apparent effective area, as shown in Figure 3.46. Beamforming complexity depends on the number of elements and the selected array architecture. For this reason, it is important to minimize the array elements, which sacrifices array performance. For instance, a square array, such as that in Figure 3.43, may not be optimum in practical applications. This is because the angular coverage in the azimuth and elevation planes will seldom be the same, and their coverage angle will also be site-dependent. In addition, the usefulness of the MIMO array will depend on the algorithm used to manage the communication signal. Thus, currently there are uncertainties about the most suitable array designs for massive-MIMO applications. The promising designs are arrays that can have flexible architectures, to be tailored later for the specific requirements of each installation site. Nevertheless, we can consider a few useful architectures. For example, in most applications the elevation pattern coverage will be smaller than the azimuth coverage. In such cases, rectangular arrays will be more appropriate than square arrays. Furthermore, some BS sites will require omni-directional azimuth coverage, which, according to Figure 3.46, will not be feasible with planar arrays. In such cases, one must Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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0 qscan = 0°

Normalized Gain (dB)

qscan = 15° –5

qscan = 30° qscan = 45°

–10

qscan = 60°

–15

–20 –90

–60

–30

0 30 q (degrees)

60

90

Figure 3.45 Scanned gain degradation of a 10-element microstrip array along its axis.

Ae-No Scan

Ae-Scanned

qscan

Figure 3.46 Reduction effective area due to its beam scan, and its effect on the array gain,  of array  2 given by G = 4π Ae /λ .

use architectures similar to the hexagonal array of Figure 3.47(a), to cover the entire coverage zone. In such an antenna architecture, the number of array faces influences the scan range of each planar array, and thus the cost and maximum gain degradation of the overall array. For the hexagonal array of Figure 3.47(b), the scan rage is limited to 30◦ , and the maximum gain degradation is about 0.6 dB, which is negligible. The above discussion provided a brief look at the antenna configurations for massiveMIMO applications. The geometries presented are by no means optimal or complete, since the requirements of massive MIMO are not fully clear yet. It emphasized phase array applications, and excluded other beam scanning architectures, especially lenses. Also, the technology and array configurations to be used are frequency-dependent. For instance, around 6 GHz, beamforming networks and antennas are reasonably well established, and mostly made of discrete components. In particular, the antenna elements are separate from the beamforming networks. This can no longer be the case in arrays for intended operation around 60 GHz. The resistive losses of the components and transmission lines will require integrated circuit and antenna architectures. These Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:04:53, subject to the Cambridge Core terms of use, available at .004

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(a)

(b)

Figure 3.47 Hexagonal array formed by six planar arrays for 360◦ coverage zone: (a) the array

geometry and (b) central beams of each hexagonal face. The scan requirement of each face is 30◦ on each side of the central beam.

differing requirements provide challenges, and opportunities for the communication and antenna communities to work together and develop a set of desirable antenna and communications requirements to guide each group to work toward resolution of the technology issues and develop practical implementations. As always, the developments will be stepwise, gradually moving toward the full implementation of massive MIMO, or its modifications for practical applications.

3.10

Summary The technology for energy harvesting and wireless communications has been briefly discussed. First, the historical background on the microwave power transmission has been introduced, which primarily concerns high-power wireless energy transmission.

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This was either between two electrical devices, or electrical energy transmission to a mechanical system, such as an aircraft. Since wireless energy transmission requires an antenna to operate, suitable antenna candidates for high-efficiency microwave power transmission were introduced both for narrowband and for wideband applications. Among the different types of antennas, microstrip patch antennas have been further investigated for wireless energy harvesting and massive-MIMO applications, in the form of single-element and array structures, respectively. In particular, three universal antenna designs have been introduced and investigated. The first two designs provided both narrowband and wideband impedance characteristics. Their design parameters have been provided and antenna performance specifications have been introduced and discussed. For these design examples, the slotted rectangular microstrip patch geometry was selected and designed with a substrate permittivity of unity, to maximize the radiation efficiency, and to allow simple frequency scaling to other frequency bands in the future. The planar configuration was selected, since it is compatible with most handheld and small communication devices, as well as implementation of large arrays for massive-MIMO applications. For convenience, the operating frequencies were selected to be centered at 1.0 GHz. The required antenna designs, for other bands, can be obtained by appropriate frequency scaling. To enhance the communication channel utilized in energy harvesting and wireless communications in general, antenna diversity has been reviewed and addressed in terms of both polarization and radiation pattern diversities. Since antenna diversity provides significant advantages in terms of communications bandwidth and quality, a third antenna design with both polarization and pattern diversities has also been provided and investigated for generating both axial and conical radiation patterns. It is an alternative to microstrip patch design and has potential for wider-bandwidth performance. The excitations of both linearly and circularly polarized applications have also been addressed for the proposed antennas. Insofar as the massive-MIMO applications are concerned, arrays of microstrip patch elements have been introduced in both planar and multi-faceted volume structures. The array scanning capabilities of planar arrays and their influences on the array gain have then been investigated and discussed. The degree of success of massive-MIMO techniques will largely depend on simultaneous beam availability, or array beam management for multiuser scenarios, over the communication coverage zones. Naturally, each requirement influences the antenna architecture and its cost. As with all other technology developments, these requirements will come in stages, and will depend on advancement in communications systems algorithms and implementation of integrated antenna arrays. For now, what we can look for is clearer antenna technical requirements, so that the antenna community can pick up the challenge and work toward developing suitable antenna candidates.

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Part II

Architectures, Protocols, and Performance Analysis

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4

Cooperative Networks with Wireless Energy Harvesting Sudha Lohani, Roya Arab Loodaricheh, Shankhanaad Mallick, Ekram Hossain, and Vijay Bhargava

4.1

Introduction Energy harvesting has emerged as one of the enabling technologies for Green Communication. As the name suggests, energy harvesting is a technique by which energy of ambient sources, for example, solar, wind, and thermal, is converted into electrical energy and used to power network equipment or mobile devices [1, 2]. This technology makes use of perpetual renewable energy sources, which reduces the consumption of high-cost constant energy sources. Lately, wireless power transfer has gained much attention in the field of energy harvesting since wireless signal is also an ambient source of energy in itself [3, 4]. Owing to the lower range of harvested energy, RF energy harvesting has potential for powering smaller network nodes. Wireless energy harvesting technology has been studied in two different paradigms of wireless communication networks. The first is simultaneous wireless information and power transfer (SWIPT) in downlink [5–7]. The SWIPT technique is used to transmit wireless energy to user equipments (UEs) whilst carrying out downlink information transmission to them as shown in Figure 4.1. The technological requirements necessary to enable this simultaneous information and energy transmission at the receiver circuit will be discussed later in this chapter. The SWIPT technique increases the energy efficiency of the network since the energy cost decreases for UEs capable of harvesting energy from the received information signal [8]. In other words, energy spent at the information transmitter is partially reused at the receiver. The reuse of energy is partial mainly because of the path-loss and non-ideal energy harvesting efficiency. On the other hand, when the UEs are carrying out uplink transmission, it is not possible to transmit energy to them using the SWIPT technique. Hence, another important paradigm of wireless energy harvesting networks is wireless-powered communication (WPC) in the uplink [9, 10]. In this technique, some fraction of the uplink transmission duration is dedicated to downlink energy transmission (DET) from the access point (AP) to the UEs. The energy harvested during this time is utilized by the UEs for uplink information transmission (UIT) to the AP in the remaining fraction of time as shown in Figure 4.2. Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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Figure 4.1 Simultaneous wireless information and power transfer (SWIPT) in downlink. The user

equipments (UEs) harvest energy from the same information signal transmitted on downlink by the access point (AP).

Figure 4.2 Wireless-powered communication (WPC) in uplink. The AP carries out downlink

energy transmission first, and then the UEs carry out uplink information transmission with the harvested energy.

Cell-edge UEs receive weak radio signal mainly due to distance-dependent attenuation. In wireless energy harvesting systems, reception of weak signals not only hampers the information transfer capacity, but also lowers the amount of energy harvested. As in traditional wireless networks, relay nodes (RNs) can play a vital role in wireless energy harvesting networks by enhancing the performance of cell-edge UEs, in terms of throughput as well as harvested energy. Interestingly, energy harvesting capability increases the willingness for cooperation among the UEs. Traditional battery-limited UEs may not be available to serve as relays for other UEs of the network. However, with the energy harvesting capability, the energy harvested from the relayed signal acts as an incentive for the UEs and increases their willingness to serve as relays. In the uplink communication of fully wireless-powered UEs, deterioration of harvested energy implies lower uplink transmit power, which in turn causes a deterioration in the information rate. For example, in [9], a severe “near–far” problem has been noticed in WPC networks since the UEs far from the AP suffer from distance-dependent 10 Mar 2017 at 08:07:55, .005

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attenuation both in DET and in UIT. Therefore, the RNs can relay the information signal as well as enhance energy harvesting by energy relaying/transmission in wirelesspowered cooperative communication networks. The focus of this chapter is on discussing different types of relay-based wireless energy harvesting networks, different relay operation policies, and resource allocation frameworks for such networks. This chapter is organized as follows. Relay-based energy harvesting systems are introduced in Section 4.2, followed by different relay operation policies in Section 4.3. Resource allocation frameworks for such relay-based wireless energy harvesting networks considering different relay operation policies are presented in Section 4.4. Finally, some open issues and challenges are discussed in Section 4.5, before we conclude the chapter in Section 4.6.

4.2

Relay-Based Energy Harvesting Systems In this section, we will discuss different means of cooperation and the roles of relays in wireless energy harvesting networks in the context of SWIPT as well as WPC. The means of cooperation can be defined in terms of relay operation policy, which will be discussed in further detail in the subsequent section.

4.2.1

Relay-based Simultaneous Wireless Information and Power Transfer (SWIPT) Networks There are various means of cooperation in relay-based wireless communication networks with SWIPT. The RNs can be designed to perform simultaneous information and energy relaying to enhance both the information capacity and the harvested energy of the UEs by exploiting spatial diversity as shown in Figure 4.3(a). In that case, the RN needs to first harvest energy from the information it is going to relay, and then forward that information with the harvested energy. Such cooperation is needed in the network where both the UEs and the RNs are energy constrained. If the RNs have their own unlimited power supply, they can be designed to perform simultaneous information relaying and power transfer to boost the information capacity and harvested energy of the UEs as shown in Figure 4.3(b) [11]. In this case, the RNs do not harvest energy from the information they are relaying. On the other hand, in a network where the UEs are not energy constrained, the RNs can be designed to perform simultaneous information relaying and energy harvesting as shown in Figure 4.3(c) [12], which adds harvested energy as an incentive for relaying the information signal. This in turn increases the number of wireless nodes willing to serve as a relay.

4.2.2

Relay-Based Wireless-Powered Communication (WPC) Networks In wireless-powered communication networks, the RNs serve both during the DET phase and during the UIT phase. If the RNs do not want to utilize their own energy, they can be designed to forward energy signals from the AP to the UEs during the DET 10 Mar 2017 at 08:07:55, .005

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(a) Simultaneous information and energy relaying. The RN relays both information and energy from the AP to the UE.

(b) Simultaneous information relaying and energy transfer. The RN relays the information signal with its own power and the UE harvests energy from the received signal.

(c) Simultaneous information relaying and energy harvesting. The RN harvests energy from the received signal and then forwards the signal to the UE. Figure 4.3 Different types of energy cooperation and transmission in a SWIPT three-node

network with an access point (AP), a relay node (RN), and user equipment (UE).

phase. In that case, the RN needs to first harvest energy from the DET signal and then forward it with the harvested energy, treating it like an information signal, as shown in Figure 4.4(a) [13]. In this way, the UEs receive energy from multiple paths, which is known as multi-path energy routing [14], and thus the amount of energy harvested during the DET phase is much higher. However, if the RNs are willing to contribute their own energy, they can be designed as supplementary sources of energy signal during the DET phase as shown in Figure 4.4(b) [10]. Since the RNs do not spend any time in harvesting energy from the AP transmission, the UEs receive much more energy to harvest. In the uplink, the RNs simply act as traditional relays. Although simultaneous information and power transfer from the UEs to the RNs is possible in the uplink, we focus our discussion on energy cooperation in the DET phase. 10 Mar 2017 at 08:07:55, .005

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(a) Downlink energy relaying with uplink information relaying. The RN relays energy signal from the AP to the UE in the downlink and relays information signal from the UE to the AP in the uplink.

(b) Downlink energy transfer with uplink information relaying. The RN transmits its own energy signal in the downlink but relays information signal from the UE to the AP in the uplink. Figure 4.4 Different types of energy cooperation and transmission in WPC three-node networks

with an access point (AP), a relay node (RN), and user equipment (UE).

In this section, we have explained that there can be different means of cooperation in wireless energy harvesting networks, mainly based on energy harvesting, transmission, and relaying at the RN. In the next section, along with a brief introduction of existing relay operation policies, we will discuss new relay operation policies based on energy cooperation.

4.3

Relay Operation Policy Several relay operation policies have been defined for conventional relay-based networks, employing different information relaying strategies. However, the introduction of the wireless power transfer feature demands the definition of new relay operation policies considering energy harvesting, relaying, and transmission at the RN. Before discussing the new relay operation policies, we will briefly discuss relay operation policies in traditional cooperative networks.

4.3.1

Conventional Cooperative Networks In terms of the duplexity of communication at the relays, the relay operation policies for conventional cooperative networks are half duplex and full duplex. Similarly, there 10 Mar 2017 at 08:07:55, .005

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are different forwarding policies such as amplify-and-forward (AF) and decode-andforward (DF). We will discuss these relaying policies briefly in the following.

4.3.1.1

Duplexity If a wireless node is capable of receiving as well as transmitting information signal in the same time frame and frequency channel, we have what is called full-duplex communication. However, if transmission and reception are separated in the time or frequency domain, then we have what is called half-duplex communication. Hence, we can distinguish between half-duplex relays and full-duplex relays [15].

Half-Duplex Relay Half-duplex transmission mode at the relay separates the reception of a signal from a source node and its forwarding to the destination, either in the time domain or in the frequency domain. For example, in half-duplex transmission in the time domain, one portion of the time frame is allocated to reception of signal from the source while the remaining portion is allocated to its transmission to the destination.

Full-Duplex Relay Full-duplex transmission enabled relay has maximum spectrum utilization since it can receive a signal from the source and forward it to the destination simultaneously in the same time frame and frequency channel. However, the interference with its own reception created by its transmission (which is referred to as self-interference) stands as a major challenge for full-duplex relaying. In this chapter, we will focus our discussion on half-duplex relay. The open issues and challenges of full-duplex relaying in wireless energy harvesting networks will be discussed toward the end of the chapter.

4.3.1.2

Forwarding Policy Different forwarding policies have been defined for the relays [16]. The most commonly analyzed forwarding policies in the literature are amplify-and-forward and decode-andforward.

Amplify-and-Forward (AF) Relay This is a simple forwarding policy in which the relay amplifies the received signal and transmits it to the destination. This improves the signal-to-noise ratio (SNR) of the signal received at the destination. The main disadvantage of this forwarding policy is that the relay amplifies the received noise signal along with the information signal, before forwarding them, which reduces the resulting SNR gain at the destination.

Decode-and-Forward (DF) Relay In this forwarding policy, the relay first decodes the received message, and then transmits the re-encoded message. In this case, the channel gain of the link between the source and the relay must be strong enough to ensure successful decoding at the relay. 10 Mar 2017 at 08:07:55, .005

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Cooperative Networks with Wireless Energy Harvesting In wireless energy harvesting systems, relay operation policies also depend on energy cooperation at the relay. If the RN is willing to contribute its own energy, it may be designed as a source of wireless energy. However, if the RN is energy constrained, it may be designed to harvest energy from the received signal and forward it to the destination. On the other hand, the RN may be designed to harvest energy from the relayed signal as an incentive to relay an information signal. Next we will discuss different relay operation policies depending on energy cooperation.

4.3.2.1

Energy Harvesting Relay Energy harvesting relay is designed to harvest energy from the relayed signal. The harvested energy acts as an incentive for relaying information to the destination. In this case, there is simultaneous information and power transfer from the AP to the RN, and the RN performs simultaneous information relaying and energy harvesting as shown in Figure 4.3(c) [12, 17, 18]. Such an energy harvesting capability at the RN provides an energy incentive for the relaying operation, which increases its willingness to participate as a relay. Such harvested energy can be stored by the RN for future use or can be immediately used to power the relay transmission. Since the RN is designed to perform simultaneous information relaying and energy harvesting, this relay operation policy is applicable in scenarios where energy harvesting at the UE is not a major concern. The RN should have a separate energy harvesting circuit. Different protocols defined to share the signal between an information transceiver and an energy harvesting circuit are discussed in the following. •

Time-Switching-Based Protocol. In the time-switching (TS)-based protocol for energy harvesting relay, each time frame is divided into two fractions. One fraction of the time frame is dedicated to harvesting energy from the AP transmission and the other is dedicated to relaying an information signal from the AP to the UE [12, 17]. This division of time is defined in terms of the time-switching fraction θ. Suppose T is the total duration of the time frame, then θT time is dedicated to harvesting energy and the remaining time (1 − θ )T is dedicated to relaying the information. θ can either be a fixed parameter or can be optimized according to the channel gain of the link between the RN and the AP as well as the available energy at the RN [17]. Let xA be the normalized information signal transmitted by the AP with power pA . The harvested energy at the RN and the information rate of the UE are given by ER = ηθTpA hAR , (4.1) 1−θ (4.2) log2 (1 + γU ), τU = 2 respectively, where γU is the SNR of the signal received at the UE in the presence of AF relay given by γU =

σ2



pA pR hAR hRU , pA hAR + pR hRU + σ 2

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(4.3)

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AP

RN qT

AP

RN

(1 – q )T/2

RN

UE

(1 – q )T/2

Figure 4.5 Energy harvesting relay protocol in SWIPT with time-switching. θ fraction of time is

dedicated by the relay node (RN) to harvest energy from the received signal from the access point (AP). Remaining (1 − θ )T time is divided equally to receive information signal from the AP and then transmit it to the user equipment (UE). Energy transmission is indicated by solid arrow and information transmission is indicated by dotted arrow.

in which σ 2 is the additive white Gaussian noise (AWGN) power. hAR and hRU are the channel gains of the links from the AP to the RN and from the RN to the UE, respectively. η is the energy harvesting efficiency of the RN and pR is the relay transmission power. The RN may be designed to store the harvested energy and utilize its own battery power for relay transmission if it is willing to contribute its own energy. Otherwise, it may be designed to power its relay transmission with the harvested energy only, i.e., pR = ER /[(1 − θ )T/2], which will be discussed in Section 4.4. It should be noted that all the mathematical deductions in this section will be done for the three-node network of Figure 4.3 with a single AP (source), an RN, and a UE (destination). We consider the case of half-duplex relays, in which the time dedicated to relay a signal from the source to the destination node is further divided into two portions for source–relay and relay–destination transmission as shown in Figure 4.5. It should be noted that, in contrast to the traditional three-node network, throughput is reduced by a factor of (1 − θ ), which is the cost of harvesting energy at the RN. In some cases, if the channel conditions or available energy at the RN cannot ensure successful relaying of the information, it is wise to keep harvesting energy instead of dividing the time between energy harvesting and information relaying. Bearing in mind this argument, we will discuss a particular time-switching protocol, named as the greedy time-switching (GS) protocol. In the GS protocol, the RN either operates in harvest as well as relay mode or only in harvest mode. If the transmission power and channel states do not ensure successful decoding at the UE, it is beneficial for the RN to keep harvesting energy all of the time, which both saves transmission energy and increases the amount of energy harvested [18]. On the other hand, if successful decoding at the UE is ensured, the RN harvests energy as well as relaying the signal. The energy harvested by the RN is given as  if γU < γth , ηTpA hAR , (4.4) ER = ηθTpA hAR , otherwise,

•

where γth is the minimum received SNR at the UE to ensure successful decoding and γU is the SNR of the signal received at the UE defined in (4.3). Power-Splitting-Based Protocol. In the power-splitting (PS)-based protocol for energy harvesting relay, the received signal power is divided into two fractions, 10 Mar 2017 at 08:07:55, .005

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AP

RN

RN

T/2

143

UE

T/2

Figure 4.6 Energy harvesting relay protocol in SWIPT with power-splitting. In the first half, the

signal received from the access point (AP) is split into two parts for energy harvesting and information decoding at the relay node (RN). Information is forwarded to user equipment (UE) in the remaining time. Energy transmission is indicated by a solid arrow and information transmission is indicated by dotted arrows.

one of which is used for decoding information and the other is used for harvesting energy. This division of power is defined in terms of power-splitting factor ρ. The portion of signal with power ρpA is used for energy harvesting and that with power (1 − ρ)pA is used for information decoding [12]. The energy harvested at the RN and the information rate of the UE are given by T ER = ηρ pA hAR , 2 1 τU = log2 (1 + γU ) , 2

(4.5) (4.6)

respectively, where γU = (1 − ρ)pA pR hAR hRU /[σ 2 ((1 − ρ) pA hAR + pR hRU + σ 2 )] is the SNR of the signal received at the UE for half-duplex AF relay. The factor of (1 − ρ) which appears in the throughput expression indicates the cost paid in terms of the information rate for harvesting energy at the RN. In half-duplex relay, the time frame is divided into two halves for source–relay transmission and relay–destination transmission. Therefore, energy is harvested for only half the total time frame, as shown in Figure 4.6, because of which the factor of 2 appears in the expression for the total energy harvested given in (4.5).

4.3.2.2

Energy Forwarding Relay Energy forwarding relay is designed to forward energy from the source node to the destination node. Unlike energy harvesting relay, whose primary purpose is to harvest energy for its own incentive, the purpose of energy forwarding relay is to maximize the energy harvested by the destination node, i.e., ultimately to prolong the battery life of the destination node. If such an RN has its own power supply and is willing to contribute energy, it is designated as an energy transmitting relay, as will be discussed further in a subsequent section. However, if the RN is energy constrained and is not willing to use its limited energy, it harvests energy from the AP transmission and then forwards that energy to the UE by transmission using the harvested energy. This is also called multi-hop energy transfer, and its advantage in terms of harvested energy has been experimentally demonstrated in [21]. Energy forwarding relay performs simultaneous information and energy relaying to the UE in SWIPT networks as shown in Figure 4.3(a). That is, the RN assists 10 Mar 2017 at 08:07:55, .005

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AP

RN

T/2

RN

UE

T/2

Figure 4.7 Energy forwarding relay protocol in SWIPT with power-splitting. In the first half, the

signal received from the access point (AP) is split into two parts for energy harvesting and information decoding at the relay node (RN). In the second half, the RN forwards the signal using the harvested energy, which is split into two parts for energy harvesting and information decoding at the user equipment (UE). Energy transmission is indicated by solid arrows and information transmission is indicated by dotted arrows.

AP

RN,UE

qT/2

AP,RN

UE

qT/2

UE

RN

(1 – q )T/2

RN

AP

(1 – q )T/2

Figure 4.8 Energy forwarding relay protocol in WPC. For θT time, the AP carries out downlink energy transmission. The RN harvests energy from the received signal for half of that time and forwards it to the UE in the remaining time. In the remaining (1 − θ)T time, the information signal is relayed from the UE to the AP. Energy transmission is indicated by solid arrows and information transmission is indicated by dotted arrows.

in both information and power transfer. The energy forwarding relay protocol with power-splitting is shown in Figure 4.7. For half-duplex energy forwarding relay performing SWIPT to the UE, the energy harvested by the RN is given by ER = ηρpA hAR T/2.

(4.7)

The energy harvested by the UE and the information rate of the UE are given by EU = η2 ρ 2 pA hAR hRU T/2, 1 τU = log2 (1 + γU ) , 2

(4.8) (4.9)

respectively, where γU = (1 − ρ)2 pA p˜ R hAR hRU /[σ 2 ((1 − ρ) pA hAR + (1 − ρ)˜pR hRU + σ 2 )] is the SNR of the signal received at the UE and p˜ R = 2ER /T is the relay transmit power due to the harvested energy. We see that the SNR of the signal received at the UE is affected by the factor (1 − ρ)2 in the numerator because energy is harvested both at the RN and at the UE. On the other hand, energy forwarding relay assists WPC networks by relaying the DET signal from the AP to the UE as shown in Figure 4.4(a). In the UIT time, the UE first transmits its information signal to the RN, which is then relayed to the AP. If θT is the allocated DET time, the RN dedicates half the time to energy harvesting and then the remaining half to forwarding that energy, as shown in Figure 4.8. For half-duplex energy forwarding relay assisting a WPC network, the energy harvested by the RN and the total energy harvested by the UE are given by 10 Mar 2017 at 08:07:55, .005

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145

T ER = ηθ pA hAR , 2

(4.10)

T EU = ηθTpA hAU + η2 θ pA hAR hRU , 2

(4.11)

respectively, where hAU is the channel gain of the link between the AP and the UE. The first part of (4.11) represents the energy harvested from the transmission of the AP while the second part represents the energy forwarded from the RN transmission. The presence of η2 in the expression for the forwarded energy and the fact that η < 1 indicates that the forwarded energy decreases rapidly with decreasing energy harvesting efficiency. However, if multiple energy forwarding relays are deployed, then much higher energy can be harvested by the UE, with much lower expenditure of energy at the AP. This is also called multi-path energy routing [14].

4.3.2.3

Energy Transmitting Relay Energy transmitting relays are designed to carry out their own energy transmission to the UEs. In SWIPT, if the RN has its own uninterrupted power supply, it is designed to forward the received signal with its own energy and hence perform simultaneous information relaying and power transfer as shown in Figure 4.3(b) [11]. The energy transmitting relay protocol for SWIPT with power splitting is shown in Figure 4.9. In the presence of half-duplex energy transmitting relay, the energy harvested by the UE and the information rate of the UE are given by T (4.12) EU = ηρpR hRU , 2 1 τU = log2 (1 + γU ) , (4.13) 2    respectively, where γU = (1 − ρ) pA pR hAR hRU / σ 2 pA hAR + (1 − ρ) pR hRU + σ 2 is the SNR of the signal received at the UE in the presence of an AF relay. As in the previous cases, the SNR is affected by the factor of (1 − ρ), which is the cost of harvesting energy at the UE. On the other hand, in WPC networks, energy transmitting relay acts as a supplementary source of RF energy as shown in Figure 4.4(b) [10]. During the DET

AP

RN

T/2

RN

UE

T/2

Figure 4.9 Energy transmitting relay protocol in SWIPT with power-splitting. In the first half of

the downlink time, the relay node (RN) receives an information signal from the access point (AP). In the remaining half of that time, the RN forwards the signal with its own power, which is split into two parts for energy harvesting and information decoding at the user equipment (UE). Energy transmission is indicated by the solid arrow and information transmission is indicated by dotted arrows. 10 Mar 2017 at 08:07:55, .005

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AP, RN

UE

UE

qT

RN (1 – q )T/2

RN

AP (1 – q )T/2

Figure 4.10 Energy transmitting relay protocol in WPC. For θT time, both the AP and the RN carry out downlink energy transmission to the UE. In the remaining (1 − θ)T time, the information signal is relayed from the UE to the AP. Energy transmission is indicated by the solid arrow and information transmission is indicated by dotted arrows.

period (say θT), the UEs receive wireless charging signal both from the AP and from the RN as shown in Figure 4.10. In that case, the energy harvested by the UE is given by EU = η (pA hAU + pR hRU ) θT.

(4.14)

In the UIT time, the UE first transmits its information signal to the RN, which is then relayed to the AP. The relay operation policies discussed in this section serve different purposes in cooperative networks with wireless energy harvesting. The main purpose of energy harvesting relay is to provide harvested energy as an incentive for serving as a relay. It is applicable in sensor or D2D networks with user cooperation. However, the incentive of harvested energy comes at the cost of the need for a complicated relay transceiver circuit design with energy harvesting capability. Energy forwarding relay enables multipath energy routing so that the destination UE can harvest a higher amount of energy. However, the energy forwarded by the RN depends largely on the energy harvesting efficiency η. Relay transceiver circuit design is another important concern in energy forwarding relay. Nevertheless, it is applicable in low-power sensor and D2D networks, where the energy requirement is low. On the other hand, energy transmitting relay significantly increases the energy harvested by the UE since it is a much nearer source of energy than the AP. However, the total network energy/power consumption increases in such cases. Therefore, it is more suitable in a fixed RN, with grid power supply or a large battery, for example, in cellular networks. The proposed relay operation policies are compared and summarized in Table 4.1. Next, we will study resource allocation problems, considering the different relay operation policies discussed in this section for cooperative networks with wireless energy harvesting.

4.4

Resource Allocation In conventional wireless networks, valuable resources such as transmission duration, frequency spectrum, and transmit power should be optimally allocated among the users of the network. With the addition of half-duplex relay, the resources are shared between source–relay and relay–destination transmissions, and this should be considered in the resource allocation problem. Optimal relay placement and relay selection are also important aspects of relay-based networks with multiple relays. With wireless power 10 Mar 2017 at 08:07:55, .005

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Table 4.1. Comparison among different relay operation policies for cooperative networks with wireless energy harvesting

Energy harvesting in RN Power supply in RN Willingness of RN to use its own energy Willingness of RN to participate in information relaying Energy harvesting in UE Power supply in UE Energy benefits in UEs

Energy harvesting relay

Energy forwarding relay

Energy transmitting relay

Yes Optional (battery) Yes if provided with energy incentive Increases (due to energy incentive) Not applicable Mandatory Not applicable

Yes Optional (battery)

No Mandatory (grid/battery) Yes

Challenges

Relay transceiver circuit design

Applicable networks

Sensor D2D

No

Increases (due to no energy cost)

Not applicable

Yes Optional Yes (provides multi-path energy routing Overcome effect of low energy harvesting efficiency in relay transceiver circuit design Sensor D2D

Yes Optional Yes (acts as supplementary energy source Minimize total energy consumption

Cellular

transfer capability, the resources are further shared between information transmission and power transmission. For example, if the time-switching protocol is used, the allocation of fractions of time dedicated to power transfer and to information transmission should result in optimal performance. Dedicating more time to power transfer could result in more energy being harvested but a deterioration of the information rate. Hence, resource allocation in cooperative networks with wireless energy harvesting capability should consider all of the aspects discussed above. In conventional cooperative networks, resource allocation takes into account different performance metrics, the information rate and power consumption being the most commonly considered ones. Optimal resource allocation is done to maximize or minimize a performance metric while ensuring that a certain constraint is imposed on the other. With power transfer capability, the amount of energy harvested is another performance metric that needs to be considered. In the following, we will describe the resource allocation problem separately for SWIPT and WPC networks with relays. First we will analyze the optimal powersplitting factor (for energy harvesting/information reception) at the RN in a three-node SWIPT network with energy harvesting relay. Then we will study a more general resource allocation problem for a network with multiple users and relays. Next, we will determine the optimal time-splitting (for downlink energy harvesting/uplink information transmission) in a three-node WPC network with energy forwarding/energy 10 Mar 2017 at 08:07:55, .005

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transmitting relay. Then we will formulate general resource allocation frameworks for a network with multiple users.

4.4.1

Resource Allocation for Relay-Based Simultaneous Wireless Information and Power Transfer Networks In simultaneous wireless information and power transfer, the same signal is shared, in the time or power domain, by the energy harvester and information decoder of a RN irrespective of whether energy harvesting relay or energy forwarding relay is concerned. Allocating more time/power to energy harvesting increases the amount of energy harvested at the RN, but lowers the end-to-end throughput. If the RN uses harvested energy only to forward the signal to the UE, allocating more time/power for information decoding at the RN results in lower end-to-end throughput because that lowers the transmission power of the RN. Thus, optimal allocation of time or power has a significant impact on the performance of the network. In this section, we focus on resource allocation for a SWIPT network with energy harvesting half-duplex DF relay. Firstly, we start with a three-node network and analyze the selection of power-splitting factors. Then we consider a general OFDMA multirelay, multiuser SWIPT network, and we optimally allocate the subcarriers, power, and the power-splitting factor, and perform optimal relay selection.

4.4.1.1

Three-node network with energy harvesting relay Consider a three-node SWIPT network with energy harvesting relay as shown in Figure 4.3(c), where the relay performs simultaneous information relaying and energy harvesting. Energy is harvested at the RN by power-splitting, and the relay operation policy is shown in Figure 4.6. A DF relaying protocol is used by the RN to forward information to the UE. The RN splits the signal received from the AP into two streams: one for harvesting the energy (E), and the other for decoding the information (I) with the fractions ρE and ρI , respectively. The harvested energy is used by the RN to forward data to the UE. The capacity of the three-node link can be calculated as τU =

  1 min log2 (1 + hAR ρI pA /(σ 2 W)), log2 (1 + hRU hAR ρE pA /(σ 2 W)) , 2 (4.15)

where W is the channel bandwidth and pA is the transmission power of the AP. This power attenuated by the fading channel in the first hop is received by the RN as hAR pA . The RN splits the received signal into two power streams with the proportions ρI and ρE , used for decoding the information and for harvesting, respectively. In the second time slot, the RN uses the harvested power given by hAR ρE pA to forward data to the UE. We assume that all energy harvested in the first time slot is used by the RN to forward the information in the second time slot. We note that the power-splitting variables are non-negative and their sum should be equal to one: ρI + ρE = 1, 10 Mar 2017 at 08:07:55, .005

(4.16)

Cooperative Networks with Wireless Energy Harvesting

(a) 5

(b)

×104

(c) 6

×104

6

2

Throughput

Throughput

Throughput

3

4

2

1 0

(e)

×104

8

6 4 2 0

0

1

Throughput

Throughput

0.5 rI

0.5 rI

1

3 2

8

4 2

0.5 rI

0

(f)

×104

0

4

1

1

6

0 0

0.5 rI

Throughput

0

(f) 8

×104

5

4

0

149

1

0.5 rI

1

0.5 rI

1

×104

6 4 2 0

0

Figure 4.11 Throughput in bits/second for varying power-splitting factor ρI for given W = 20, 000 Hz, SNR = 100, and hAR = 1 for different hRU : (a) hRU = 13 , (b) hRU = 12 , (c) hRU = 1, (d) hRU = 2, (e) hRU = 3, and (f) hRU = 4.

i.e., the splitter is not producing any energy and power wastage is ignored. Figure 4.11 analytically shows the optimal splitting factor for different channel realizations. As depicted in the figure, the optimal splitting factor depends on the channel gain from the RN to the UE.

4.4.1.2

Multiuser network with multiple energy harvesting relays Here, we consider a more general downlink system model with one AP, multiple RNs, and multiple UEs, as shown in Figure 4.12. We assume that the transmissions of the RNs and the AP are orthogonal over N subcarriers, each of them with a bandwidth of W. The number of RNs is assumed to be M, and the number of UEs is K. When cooperation is beneficial for a UE node, an RN assists its transmission. A DF relaying protocol is used here as well when cooperation is beneficial. We decide whether to cooperate or not depending on the channel conditions. We denote the RNs by m, and the UEs by k. The transmission modes corresponding to cooperative and non-cooperative behavior are superscripted with (C) and (NC), respectively. The channel gains from the AP to i,(C,1) i,(C,2) the RN m and from the RN m to the UE k are defined as hA,m and hm,k , respectively. The superscripts i, (C, 1) and i, (C, 2) indicate the cooperative transmission mode over 10 Mar 2017 at 08:07:55, .005

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Figure 4.12 Downlink information relaying with energy harvesting in a multiuser SWIPT network with one access point (AP), three relay nodes (RNs), three items of user equipment (UE1–3), and five subcarriers.

subcarrier i in time slots one and two, respectively. Similarly, the channel gain for the i,(NC) non-cooperative (direct) link is defined as hA,k . Since the RNs are assumed to have power-splitting receivers, in the case of cooperative transmission, the signal received from the AP is split into two streams: one for harvesting energy (E), and the other for decoding information (I) with the proportions i,(E) i,(I) and ρm,k , respectively. The harvested energy is used by the RNs only to forward ρm,k data to the UE nodes. Here, we formulate the resource optimization problem, where the objective is to maximize the total capacity of the system. The capacity of the cooperative link can be calculated as    1 1 i,(C,1) i,(I) i,(C) i,(C) τm,k = min log2 1 + 2 hA,m ρm,k pA,m , 2 σ W   1 i,(C,2) i,(C,1) i,(E) i,(C) , (4.17) log2 1 + 2 hm,k hA,m ρm,k pA,m σ W i,(C)

where pA,m is the transmission power of the AP on subcarrier i over the cooperative link to send data for RN m. This power attenuated by the fading channel in the first i,(C,1) i,(C) hop is received by RN m as hA,m pA,m . The received signal is split into two power 10 Mar 2017 at 08:07:55, .005

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i,(I)

i,(E)

i,(I)

151

i,(E)

streams with proportions ρm,k and ρm,k , where ρm,k and ρm,k are used for decoding the information and for harvesting, respectively. In the second time slot, the RN uses the i,(E) i,(C) harvested power given by hi,(C,1) A,m ρm,k pA,m to forward data to UE k. Here we assume that all energy harvested in the first time slot is used by RN m to forward information in the second time slot. This assumption simplifies the problem insofar as resources can be optimized over each transmission frame. Otherwise, if we assume that the RNs are capable of harvesting energy for use in the future, dynamic programming is required to tackle the problem. If the direct link is better than the cooperative link, the AP directly transmits data to the UE. The capacity of the direct link is calculated as   1 i,(NC) i,(NC) i,(NC) = log2 1 + 2 hA,k pA,k , (4.18) τk σ W i,(NC)

where pA,k is the transmission power of the AP on subcarrier i over direct link to the UE k. Our objective is to maximize the total capacity of the system subject to the power constraint of the AP. The joint optimization problem of subcarrier assignment, power allocation, transmission mode (cooperative or non-cooperative) and relay selection is formulated as maximize

N K  M  

P,S,ρ

subject to C1 : C2 : C3 : C4 : C5 : C6 : C7 :

i,(C) i,(C)

sm,k τm,k +

K  N 

i,(NC) i,(NC) τk

sk

k=1 m=1 i=1 k=1 i=1 N M N K K    i,(C) i,(C)   i,(NC) i,(NC) sm,k pA,m + sk pA,k k=1 m=1 i=1 k=1 i=1   i,(C) i,(NC) sm,k , sk ∈ 0, 1 , ∀i, k, m, M K  K   i,(C) i,(NC) sm,k + sk ≤ 1, ∀i, k=1 m=1 k=1 i,(I) i,(E) i,(C) ρm,k + ρm,k = sm,k , ∀i, k, m, i,(C) i,(NC) i,(I) i,(E) pA,m , pA,k , ρm,k , ρm,k ≥ 0, ∀i, k, m, N K   i,(C) sm,k ≤ nm , ∀m, k=1 i=1 i,(C,1) i,(I) i,(C,1) i,(C,2) i,(E) hA,m ρm,k = hA,m hm,k ρm,k , ∀i, k, m,

≤ pmax ,

(4.19)

where P, ρ, and S denote power allocation, power-splitting factors, and subcarrier allocation policy, respectively. C1 is the power constraint, where pmax is the power budget i,(NC) are binary integer variables (indicators). If the of the AP. C2 shows that si,(C) m,k and sk i,(C)

AP is transmitting to UE k with the assistance of RN m over subcarrier i, sm,k is one; i,(NC)

is defined for non-cooperative transmission. C3 otherwise it is zero. Similarly, sk implies that each subcarrier can be used only once, in order to avoid interference. It also states that over each subcarrier either cooperative or non-cooperative mode can be used. 10 Mar 2017 at 08:07:55, .005

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C4 indicates that the sum of the power-splitting ratio in each subcarrier should be equal to one if that subcarrier is selected for cooperation, i.e., the splitter is not producing any energy and power wastage is ignored. C5 states that the power and splitting variables are non-negative. C6 indicates that each relay can assist only over nm subcarriers due to the limitations of the power-splitter and the capacity of the energy harvester, where nm is known a priori. To avoid information loss and wastage of power at the relays here again, we have incorporated C7 into our formulation. It should be noted that the amount of energy harvested of each RN is not considered in a separate constraint because it determines the RN’s transmit power, which is reflected in the throughput expression in the objective function. The problem stated above is a mixed integer non-linear program (MINLP), which is very difficult to solve in general. In [22], it is shown how to solve this problem optimally using a dual decomposition technique. In order to solve the problem, first we obtain the power-splitting ratios for each cooperative link from C4 and C7 as i,(C,2)

i,(I)∗ ρm,k = i,(E)∗ ρm,k

=

hm,k

i,(C,2)

1 + hm,k 1

1 + hi,(C,2) m,k

, (4.20) .

Since we have optimally obtained the splitting factors in (4.20), the variables of the optimization problem in (4.19) are reduced to (P, S), i.e., the transmission power and subcarrier allocation policy. The major concern for solving problem (4.19) is the integer subcarrier assignment variables and constraints. Next, we relax the indicators S in the interval [0, 1] and define i,(C) i,(C) i,(C) i,(NC) i,(NC) i,(NC) pA,k = sk pA,k to make the auxiliary power variables  pA,m = sm,k pA,m and  optimization problem tractable. Note that the resulting optimization problem becomes convex with respect to the auxiliary and relaxed variables given by  P and S, respectively. The relaxed optimization problem is convex with respect to ( P, S) and strong duality holds, i.e., the duality gap is zero. Therefore, we can solve the Lagrangian dual problem and still obtain the optimal solution of the relaxed problem [22]. An optimal subcarrier allocation policy based on the Hungarian algorithm [23] is proposed in [22]. The Hungarian method is used to find the optimal solution for linear assignment problems with polynomial complexity. It can be proved that the solution of the relaxed problem is optimal and has integer values, and, hence, we can obtain the optimal solution of the original problem (4.19). The proof is based on the concept of total unimodularity [24]. The proof of convexity and optimality of the solution for integer variables can be derived as in [25].

Example 4.1 In this example, we compare the performance of the proposed SWIPT network with energy harvesting relay with that of a conventional relay-based network. We assume that in both cases pmax is the limit on the total power budget of the system. The AWGN 10 Mar 2017 at 08:07:55, .005

Average energy efficiency [bits / Joule]

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153

8000 N = 16, proposed scenario

7000

N = 32, proposed scenario

6000

N = 64, proposed scenario

5000

N = 16, No harvesting scenario N = 32, No harvesting scenario

4000

N = 64, No harvesting scenario

3000 2000 1000 0 45

50 Pmax(dBm)

55

Figure 4.13 Average energy efficiency versus pmax for different numbers of subcarriers.

power (σ 2 ) and bandwidth of each subcarrier (W) are assumed to be 5 × 105 W/Hz and 20 kHz, respectively. The number of UEs in each group is eight, i.e., M = K = 8, and the number of subcarriers for each relay (nm ) is 4. Figure 4.13 shows the energy efficiency in terms of pmax for different numbers of subcarriers. The energy efficiency is defined as τT /pT , where τT is the total system capacity and pT is the total power consumed in the system. pT contains both the transmission and the constant power of all the nodes. We compare the proposed scheme with a scenario where there is no energy harvesting. As shown in Figure 4.13, the proposed scheme performs slightly better than “no harvesting” scenarios in terms of energy efficiency. It is worth mentioning that the proposed energy harvesting scheme outperforms the “no harvesting” scenario in terms of fairness, since the RNs do not spend their energy for the purpose of relaying.

4.4.2

Resource Allocation in Relay-Based Wireless-Powered Communication Networks In wireless-powered communication, the UEs share the available uplink time between the energy harvester and the information transmitter. If the uplink transmission is fully wireless-powered, then for maximization of the information capacity one needs the optimal amount of harvested energy as well as the optimal transmission time. For example, allocating more time for information transmission does not necessarily increase the information capacity because it implies a reduction in energy harvesting time and hence a reduction in uplink transmission power. Hence, for maximization of the information capacity one requires optimal allocation of time for energy harvesting as well as information transmission. In the following, we will perform optimal time allocation in a three-node WPC network with energy forwarding, half-duplex, AF relay. Then we will extend the problem to a general multiuser network. Next, we will perform optimal time allocation in a 10 Mar 2017 at 08:07:55, .005

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three-node WPC network with energy transmitting, half-duplex, AF relay. Then we will study a general time and power allocation problem for a multiuser scenario.

4.4.2.1

Three-Node Network with Energy Forwarding Relay Consider a three-node WPC network with one AP, one UE, and one energy forwarding relay, as shown in Figure 4.4(a), where the RN performs downlink energy relaying and uplink information relaying. The energy forwarding relay protocol is given in Figure 4.8. The amount of energy harvested by the UE in the DET phase is given by EU = ηθTpA hAU + η2 θ (T/2)pA hAR hRU in (4.11). Uplink information transmission of the UE is powered by harvested energy (EU ) and assisted by the AF relay. The signal received at the AP is given by [26]  pR pU hRU hAR yA = xu + n˜ w , (4.21) pU hRU + σ 2 where xu is the unit-power baseband information signal transmitted by the UE, n˜ w ∼ CN (0, σ 2 (1 + pR hAR /(pU hRU + σ 2 )) is the amplified AWGN noise, pU = 2EU /((1 − θ )T) = 2ηθTpA (hAU + ηhAR hRU /2)/((1 − θ )T) is the uplink transmission power of the UE, and pR is the relay transmission power. Now, the information capacity of the UE is given by τU =

1−θ log2 (1 + γU ), 2

(4.22)

where pR pU hRU hAR  pR hAR + pU hRU + σ 2 μ1 μ2 θ T = 2 , σ (μ1 (1 − θ )T + μ2 θT)

γU =

σ2



(4.23)

in which μ1 = pR hAR , μ2 = 2ηpA (hAU + ηhAR hRU /2) hRU , and the higher-order term σ 4 is ignored, assuming it to be much lower than the signal power. Let us denote the DET time by tdl and the UIT time by tul , i.e., tdl = θ T and tul = (1 − θ )T. We formulate a general expression for the throughput as follows:   tul μ1 μ2 tdl τU = log2 1 + 2 . (4.24) 2T σ (μ1 tul + μ2 tdl ) Our goal is to find the optimal time allocation that maximizes the uplink throughput of the UE. Therefore, the following optimization problem is formulated: maximize τU tdl ,tul

subject to C1 : tdl + tul ≤ T, C2 : tdl , tul ≥ 0. 10 Mar 2017 at 08:07:55, .005

(4.25)

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The constraint C1 establishes that the total uplink time T is limited and C2 ensures non-negativity of time variables. It should be noted that the harvested energy is not individually considered in the optimization problem. This is because the throughput of the UE depends upon the harvested energy in WPC networks and, hence, maximizing the throughput indirectly implies maximizing the harvested energy as well. The objective function is convex. The Lagrangian of the problem is written as [27]   tul μ1 μ2 tdl (4.26) log2 1 + 2 − ν (tdl + tul − T) . L (tdl , tul , ν) = 2T σ (μ1 tul + μ2 tdl ) Since the problem is convex, the solution can be found by using Karush–Kuhn–Tucker (KKT) conditions [27] and solving the resulting equations as shown in [10].

Example 4.2 In this example, we analyze the performance of an energy forwarding relay-based threenode WPC network with varying distance of the UE from the AP. We also compare the performance with that of a non-cooperative WPC network. Here, we assume T = 1, η = 50%, and pA = 20 W. It is observed that, in the non-cooperative network, a significant portion of the available time is dedicated to the DET, with a very small portion dedicated to the UIT as can be seen in Figure 4.14. Therefore, the time-splitting ratio θ → 1 to achieve optimal throughput performance. However, in the presence of energy forwarding relay, the DET time is significantly reduced, which allows more time for the UIT. This is because, by forwarding the DET signal of the AP, the RN allows the UE to harvest more energy in a shorter time. Also, the UE can carry out uplink transmission with much lower energy when the RN is present to forward its information to the AP. As we can see in Figure 4.15, energy forwarding relay significantly increases the throughput performance of the UE. With increasing distance of the UE from the AP, throughput degradation is

Figure 4.14 DET and UIT time allocation versus UE distance.

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1.4 EF Relay, PR = 15 W EF Relay, PR = 10 W EF Relay, PR = 5 W NO Relay

Throughput (bps / Hz)

1.2 1 0.8 0.6 0.4 0.2 0 30

35

40

45

50

Distance of UE from AP (m) Figure 4.15 Throughput versus UE distance.

faster in the presence of relay. This is because increasing distance decreases the energy harvested from the RN as well as the AP. It also causes a deterioration of the uplink transmission link of the UE to the RN. The variation of the RN uplink transmit power has almost no effect on the throughput performance of the UE. This shows that the main impact on the throughput performance is in the DET phase, which defines the harvested energy and hence uplink transmission power of the UE.

4.4.2.2

Multiuser Network with Energy Forwarding Relay Let us consider a scenario with one AP, one energy forwarding relay, and K UEs, solely relying on wireless energy harvesting to power their uplink transmission. The system model and relay protocol are presented in Figures 4.16 and 4.17, respectively. As described for three-node networks, the AP transmits the wireless charging signal and the UEs harvest energy for the DET time tdl which is a fraction of the total uplink transmission time, i.e., tdl = θ T. After harvesting energy from the AP transmission for time tdl /2, the RN forwards that energy to the UEs during the rest of the DET time. Uplink transmissions of the UEs are orthogonal in the time domain and their (UIT) times are denoted by tul(k) , k ∈ {1, 2, . . . , K}. Signals received from the UEs are amplified and forwarded by the RN to the AP. The channel power gains of the links from the kth UE to the AP and the RN are given by hAU(k) and gRU(k) , respectively. The total energy harvested by the kth UE, as given in (4.11), is given by   ηhAR hRU(k) (4.27) t(dl) , ∀k. EU(k) = ηpA hAU(k) + 2 Let the unit-power equivalent baseband signal transmitted by each UE in the first phase of its UIT time be denoted by xU(k) . In the second phase of its UIT time, the signal 10 Mar 2017 at 08:07:55, .005

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RN UE1

AP UEk Uplink Information Transmission Downlink Energy Transmission Figure 4.16 Downlink energy relaying and uplink information relaying in a multiuser WPC network with an access point (AP), a relay node (RN), and multiple user equipments (UEs).

AP

all UE UE1

RN, all UE AP, RN tdl / 2

tdl / 2

RN

AP

UEk

t1(ul)

RN

AP

tk(ul)

T Figure 4.17 Energy forwarding relay protocol in a multiuser WPC network. tdl is the downlink energy transmission time, and tk(ul) is the uplink information transmission time of the kth UE.

received from each UE is amplified and forwarded to the AP by the RN with power pR . The signal received at the AP is given by [26]  yR(k) =

pR pU(k) hAR hRU(k) xU(k) + n˜ w , ∀k, pU(k) hRU(k) + σ 2

    where n˜ w ∼ CN 0, σ 2 1 + pR hAR / pU(k) hRU(k) + σ 2 is the amplified AWGN and pU(k) = 2EU(k) /tul(k) is the uplink transmission power of the UE due to harvested energy. Therefore, the SNR of the signal received at the AP is given by γU(k) =

σ2

μ1 μ2(k) tdl  , ∀k, μ2(k) tdl + μ1 tul(k)



(4.28)

  where μ1 = pR hAR and μ2(k) = 2ηpA hAU(k) + ηhAR hRU(k) /2 hRU(k) . Using (4.28), the throughput of each UE in bps/Hz is given by   tul(k) log2 1 + γU(k) 2T   tul(k) μ1 μ2(k) tdl  , ∀k. = log2 1 + 2  2T σ μ2(k) tdl + μ1 tul(k)

τU(k) =

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(4.29)

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The optimal DET time and UIT time of each UE is determined by formulating the following optimization problem:   maximize U τU(1) , . . . , τU(k) tdl ,tul

subject to C1 : tdl +

K k=1

tul(k) ≤ T

C2 : tdl ≥ 0; tul(k) ≥ 0, ∀k,

(4.30)

where tul = {tdl , tul(1) , . . . , tul(k) }. Constraint C1 indicates the limitation of total uplink transmission time,while C2 ensures the non-negativity of the optimization variables.  U τU(1) , . . . , τU(k) is a utility function of the throughput of all UEs which, for instance, can be simply a sum function. The solution approach is similar to the previous problem in that case.

Example 4.3 In this example, we perform the optimal resource allocation by solving the optimization problem in (4.30) using the following objective function: K    U τU(1) , . . . , τU(k) = τU(k) . k=1

Figure 4.18 indicates that the average throughput is much higher in the relay-based WPC networks, as was observed in the three-node network. The average throughput decreases with increasing number of UEs because the UIT time of each UE as well as the total DET time decrease to accommodate uplink transmission of an increasing number of UEs. Additionally, the throughput performance increases with increasing energy harvesting efficiency in a logarithmic fashion. It should be noted that the effect of the energy harvesting efficiency is highly remarkable in the relay-based network. 0.07 Average throughput (bps / Hz)

158

EF Relay, n = 1 EF Relay, n = 0.75 EF Relay, n = 0.5 EF Relay, n = 0.25 No Relay, n = 1 No Relay, n = 0.75 No Relay, n = 0.5 No Relay, n = 0.25

0.06 0.05 0.04 0.03 0.02 0.01 0

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Number of users Figure 4.18 Average throughput versus number of UEs.

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This is because the RN first harvests energy and then forwards it to the UE, which again harvests that energy, as indicated in (4.27). Thus the throughput of the UE depends largely on the energy harvesting efficiency.

4.4.2.3

Three-Node Network with Energy Transmitting Relay Consider a three-node WPC network with one AP, one UE, and one energy transmitting relay as shown in Figure 4.4(b), where the RN performs downlink energy transfer and uplink information relaying. The relay protocol is shown in Figure 4.10. The energy harvested by the UE from the AP and the RN transmission is given by EU = η (pA hAU + pR hRU ) θT in (4.14). Uplink information transmission of the UE is powered by the harvested energy (EU ) and assisted by the AF relay. The signal received by the AP is given by [26]  yA =

pR pU hRU hAR xd + n˜ w , pU hRU + σ 2

(4.31)

where n˜ w ∼ CN (0, σ 2 (1 + pR hAR /(pU hRU + σ 2 )) is the amplified AWGN, pU = 2EU /((1 − θ )T) = 2η (pA hAU + pR hRU ) θT/((1 − θ )T) is the uplink transmit power of the UE, and pR is the relay transmission power. The information capacity of the UE is given by τU =

1−θ log2 (1 + γU ) , 2

(4.32)

where γU =

pR pU hRU hAR   σ 2 pR hAR + pU hRU + σ 2

=

μ1 μ2 θT , σ 2 (μ1 (1 − θ )T + μ2 θT)

(4.33)

in which μ1 = pR hAR , μ2 = 2η (pA hAU + pR hRU ) hRU , and the higher-order term σ 4 is ignored, assuming it to be much lower than the signal power. The formulation of the optimization problem and the solution approach are similar to those for the problem in (4.25) and can be used to find the optimal time allocation that maximizes the information capacity of the UE.

Example 4.4 In this example, we maximize the throughput of the UE in energy transmitting relaybased three-node WPC networks. We analyze the time allocation and throughput performance and then compare it with that of a non-cooperative WPC network. From Figure 4.19, it is observed that the DET time is remarkably lower and the UIT time is much higher in the presence of energy transmitting relay. Since the RN transmits its own DET signal, the UE can harvest energy in much less time than in 10 Mar 2017 at 08:07:55, .005

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Figure 4.19 DET and UIT time allocation versus UE distance.

4 ET Relay, pR = 15 W ET Relay, pR = 10 W ET Relay, pR = 5 W No Relay

Throughput (bps / Hz)

3.5 3 2.5 2 1.5 1 0.5 0 30

35

40

45

50

Distance of UE from AP (m) Figure 4.20 Throughput versus UE distance.

the non-cooperative scheme. This allows more time for uplink transmission of the UE. As a result, the throughput also significantly improves in the relay-based network, as can be observed in Figure 4.20. We observe a logarithmic increase in throughput performance with increasing RN transmit power. A higher RN transmit power means more energy harvested by the UE, which in turn increases its uplink transmit power.

4.4.2.4

Multiuser Network with Energy Transmitting Relay Let us consider a network with an AP, an energy transmitting relay, and K UEs solely powered by harvested energy. The system model and relay protocol are presented in 10 Mar 2017 at 08:07:55, .005

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RN UE1

AP UEk Uplink Information Transmission Downlink Energy Transmission Figure 4.21 Downlink energy transmission and uplink information relaying in a multiuser WPC network with an access point (AP), a relay node (RN), and multiple user equipments (UEs).

RN

all UE

tdl

UE1

RN

AP

t1(ul)

UEk

RN

AP

tk(ul) T

Figure 4.22 Energy transmitting relay protocol in multiuser WPC networks. tdl is the downlink

energy transmission time, and tk(ul) is the uplink information transmission time of kth UE.

Figures 4.21 and 4.22, respectively. If the RN has an unlimited power supply, the resource allocation problem becomes simply the optimal time allocation problem [10]. However, limited availability of energy requires optimal allocation of the RN transmit power along with the DET and UIT time. In this system model, we consider limited availability of energy at the RN and propose an optimal time and power allocation solution. The case with an unlimited power supply becomes an optimal time allocation problem, which can easily be deduced from our proposed solution. Since the RN is energy transmitting relay, during the DET time, it transmits a wireless charging signal with power pRD . During this time, all UEs harvest energy from the received signal. In this case, assuming high path loss in the direct link from the AP to the UEs, only the RN transmission is considered in the DET phase. In the uplink, the RN relays each UE transmission using the transmit power pRU(k) . The rest of the assumptions are similar to those discussed in the previous resource allocation problems. The energy harvested by the UEs is given by EU(k) = ηpRD hRU(k) tdl , ∀j.

(4.34)

Following a similar analysis to that in the previous resource allocation problems, for the UE uplink transmission, the SNR of the signal received at the AP is given by [26] 10 Mar 2017 at 08:07:55, .005

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γU(k) =

σ2

μ1 μ2(k) pRD pRU(k) tdl  , ∀k, μ2(k) pRD tdl + μ1 pRU(k) tul(k)



(4.35)

where μ1 = hAR and μ2(k) = 2ηh2RU(k) . Using (4.35), the throughput (bps/Hz) of each UE is written as   tul(k) log2 1 + γU(k) , 2T   tul(k) μ1 μ2(k) pRD pRU(k) tdl  , ∀k. = log2 1 + 2  2T σ μ2(k) pRD tdl + μ1 pRU(k) tul(k)

τU(k) =

(4.36)

The optimal DET time and UIT time of the UEs as well as the RN transmit power can be determined by formulating the following optimization problem:   maximize U τU(1) , . . . , τU(k) tdl ,tul ,PR

subject to C1 : tdl +

K 

tul(k) ≤ T,

k=1

C2 : pRD tdl +

K 

pRU(k) tul(k) /2 ≤ Emax ,

k=1

C3 : pRD ≤ pmax , C4 : pRU(k) ≤ pmax , ∀k, C5 : tdl ≥ 0; tul(k) ≥ 0, ∀k, C6 : pRD ≥ 0, pRU(k) ≥ 0, ∀k,

(4.37)

where PR represents the RN transmit power variables. C1 represents the limited availability of DET and UIT time, and C2 represents the limited availability of energy at the RN. C3 and C4 represent the peak power constraint on the RN transmit power. C5 and constraints C6 impose non-negativity  on power variables and time variables. Even if the  utility function, U τU(1) , . . . , τU(k) , is simply a sum function, the objective function is highly non-convex. However, the change of variables pRD tdl = ERD , pRU(k)

tul(k) = ERU(k) 2

(4.38) (4.39)

can make the problem convex. With the given change of variables, the throughput of each UE can be re-written as   tul(k) 2μ1 μ2(k) ERD ERU(k)   , ∀k. τU(k) = log2 1 + 2 (4.40) 2T σ tul(k) μ2(k) ERD + 2μ1 ERU(k) 10 Mar 2017 at 08:07:55, .005

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The resulting optimization problem can be written as follows:   maximize U τU(1) , τU(2) , . . . , τU(K) tdl ,tul ,ER

subject to C1 : tdl +

K 

tul(k) k=1 K 

C2 : ERD +

≤ T,

ERU(k) ≤ Emax ,

(4.41)

k=1

C3 : ERD − pmax tdl ≤ 0, C4 : ERU(k) − pmax tul(k) /2 ≤ 0, ∀k, C5 : tdl ≥ 0; tul(k) ≥ 0, ∀k, C6 : ERD ≥ 0, ERU(k) ≥ 0, ∀k, where ER represents the energy variables and the constraints are changed accordingly. The new optimization problem is convex and can be solved using KKT conditions [27] as shown in [28].

Example 4.5 In this example, we perform optimal resource allocation by solving the optimization problem (4.41) using the following objective function: K    U τU(1) , . . . , τU(k) = τU(k) . k=1

In Figure 4.23, we analyze the throughput performance of an energy transmitting relay-based WPC network in the presence of a varying number of UEs, with

Average throughput (bps / Hz)

0.09 ET Relay, Emax = 20 J ET Relay, Emax = 15 J ET Relay, Emax = 10 J No Relay

0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

2

3

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7

8

9

10

Number of users Figure 4.23 Average throughput versus number of UEs.

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varying Emax , and also compare it with the performance of non-cooperative WPC networks. With the increase in Emax , the average throughput of the UEs increases in logarithmic fashion. This is because the higher the available energy at the RN, the greater the energy harvested by the UEs, which means higher uplink transmit power of the UEs. The uplink transmit power of relays while relaying UIT of the UEs also increases with increasing available energy at the RN. As in the case of a multiuser network with energy forwarding relay, the average throughput decreases with increasing number of UEs.

4.5

Open Issues and Challenges Wireless energy harvesting technology is a new research topic, and many open issues and challenges remain to be solved. Since most of the existing literature proposes sharing of signal in the time or power domain between the energy harvester and information receiver, the rate–energy tradeoff is one of the major concerns in wireless energy harvesting communication networks. Therefore, a new receiver circuit design with integrated capability of harvesting energy and decoding information is necessary [5]. The existing low energy harvesting efficiency significantly curtails the performance of energy harvesting networks and demands more research in the area of hardware circuit design. One way of compensating for low energy efficiency is transmitting a highpower charging signal. But health and safety issues limit that approach too. Cooperative networks with wireless energy harvesting bring forward several issues in the paradigm of interference management and full-duplex communications. We will discuss these issues in the following.

4.5.1

Full-Duplex Communications In full-duplex communications, a wireless node can transmit and receive simultaneously using the same frequency channel. Since full-duplex communication ideally doubles the spectral efficiency, numerous research works have investigated its potential performance gain and technical challenges [19, 29, 30]. In wireless energy harvesting networks, full duplexity can also be exploited in simultaneous information transmission and energy reception or vice versa. One of the major implementation challenges of full-duplex communication is the high self-interference between the transmitter and receiver of the same wireless node. The wireless node, which is transmitting the energy harvesting signal, creates self-interference with the received information signal. Nevertheless, larger nodes can exploit the advantages of full duplexity by spatially separating the receiving and transmitting antennas and applying advanced interference cancellation techniques [15]. However, self-interference cancellation techniques in smaller wireless nodes are of high importance to exploit the full spectral advantage of full-duplex communication [31, 32]. In traditional cooperative networks, full duplexity at the RN implies simultaneous information reception from the source and transmission to the destination, which can be inherited in wireless energy harvesting cooperative networks [19]. However, with the 10 Mar 2017 at 08:07:55, .005

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AP

RN

RN

UE

AP

RN

T/2

165

T/2

Figure 4.24 Full-duplex simultaneous energy harvesting and information relaying in a three-node SWIPT network. During the second half of the time, the relay node (RN) receives the energy harvesting signal from the access point (AP) while forwarding the information signal to user equipment (UE). Energy transmission is indicated by the solid arrow and information transmission is indicated by dotted arrows.

UE

RN

RN

AP

AP, RN

UE

AP

UE, RN

T/2

T/2

Figure 4.25 Full-duplex downlink energy transmission and uplink information relaying in a three-node WPC network. During the first half of the time, the UE simultaneously receives energy harvesting signal from the AP and the RN while transmitting the information signal to the RN. During the remaining half, the RN simultaneously receives the energy harvesting signal from the AP while forwarding the information signal to the AP. Energy transmission is indicated by solid arrows and information transmission is indicated by dotted arrows.

energy harvesting capability, the RN can simultaneously receive energy from the AP while transmitting information to the UE as shown in Figure 4.24 [20]. Such a protocol eliminates the issue of self-interference and the need to split the signal between the information receiver and the energy harvester. However, the full duplexity is underutilized since the RN simultaneously receives and transmits only in the second half of the time frame. Similarly, in WPC networks, the RNs can simultaneously transmit energy to the UEs while receiving uplink information from them, and also simultaneously receive energy from the AP while forwarding information to the AP as shown in Figure 4.25. Hence, there is no need to separate DET time and UIT time. Thus, full-duplex communication makes available several opportunities in wireless energy harvesting cooperative networks, for both downlink and uplink communication. However, efficient self-interference cancellation techniques are necessary in order to fully exploit the advantages.

4.5.2

Interference Management Because of high spectral efficiency, universal frequency reuse is highly desirable in a multi-cell environment. However, the spectral efficiency comes at the price of higher inter-cell interference. In cooperative wireless energy harvesting networks, the proximity of dedicated RNs of neighboring cells increases the amount of interference received 10 Mar 2017 at 08:07:55, .005

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by the cell-edge users. The signal received by the RN is also subject to interference due to transmissions from neighboring base stations. For example, throughput expressions given in the resource allocation framework of SWIPT need to include the interference signal received by the UEs from the neighboring RNs using the same frequency channel as well as that received by the RNs from the neighboring BS transmissions. It should be noted that interference management is viewed from a different perspective in wireless energy harvesting networks. While the interference signal causes a deterioration of the throughput performance, the amount of energy harvested increases because of it [33, 34]. Therefore, interference management should be performed to attain an optimal tradeoff between the throughput performance and the harvested energy metric. Moreover, if the RN uses that harvested energy for information relaying, the resource allocation parameters become highly entangled with each other. In that case, the optimal allocation of time, subcarrier, and BS/RN transmit powers discussed in the previous sections becomes a highly non-convex problem that is very difficult to solve. Successive convex approximation is used in [35] for a downlink SWIPT network with energy harvesting relay for a single-user/single-relay scenario for joint resource allocation. A game-theoretic approach is presented in [36] for a similar scenario. However, the multiuser, multi-relay case in a multi-cell environment generates very complex resource allocation problems. Finding low-complexity optimal solutions to such problems is a promising area of future research.

4.6

Summary We have studied relay-based cooperative networks with wireless energy harvesting technology. The roles of relays can be significantly different in wireless energy harvesting networks; for example, relays can harvest energy from the information signal, transmit their own energy signal, or simply forward the received energy with information. To address these issues, new relay configurations and their operation policies have been introduced in the context of SWIPT in downlink as well as WPC in uplink. The problem of radio resource allocation for SWIPT and WPC has been studied in detail, considering different relay operation policies. First, we designed resource allocation frameworks for the simplest three-node network topology with a single source, relay, and destination node. Our objective was to show how the radio resources can be optimally allocated so that the overall system performance is improved in terms of both information transmission and energy harvesting for SWIPT as well as WPC networks. Then we developed efficient resource allocation frameworks for a general setup with multiple users and relay nodes. Numerical examples have shown the effectiveness of our proposed resource allocation frameworks. Full-duplex communications is a promising technology to enhance the performance of cooperative wireless energy harvesting networks. However, owing to several research challenges, it remains an open research problem and demands in-depth future research. Interference management in multi-relay/multi-cell environments is also an interesting open research problem relating to cooperative energy harvesting networks. 10 Mar 2017 at 08:07:55, .005

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References [1] P. T. V. Bhuvaneswari, R. Balakumar, V. Vaidehi, and P. Balamuralidhar, “Solar energy harvesting for wireless sensor networks,” in Proc. 1st International Conference on Computational Intelligence, Communication Systems and Networks (CICSYN ’09), July 2009, pp. 57–61. [2] R. Kappel, W. Pachler, M. Auer et al., “Using thermoelectric energy harvesting to power a self-sustaining temperature sensor in body area networks,” in Proc. IEEE International Conference on Industrial Technology (ICIT), February 2013, pp. 787–792. [3] L. Varshney, “Transporting information and energy simultaneously,” in Proc. IEEE International Symposium on Information Theory (ISIT), July 2008, pp. 1612–1616. [4] H. Jabbar, Y. Song, and T. Jeong, “RF energy harvesting system and circuits for charging of mobile devices,” IEEE Transactions on Consumer Electronics, vol. 56, no. 1, pp. 247–253, February 2010. [5] X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power transfer: Architecture design and rate-energy tradeoff,” IEEE Transactions on Communications, vol. 61, no. 11, pp. 4754–4767, November 2013. [6] K. Huang and E. Larsson, “Simultaneous information and power transfer for broadband wireless systems,” IEEE Transactions on Signal Processing, vol. 61, no. 23, pp. 5972–5986, December 2013. [7] R. Zhang and C. K. Ho, “MIMO broadcasting for simultaneous wireless information and power transfer,” IEEE Transactions on Wireless Communications, vol. 12, no. 5, pp. 1989– 2001, May 2013. [8] D. W. K. Ng, E. S. Lo, and R. Schober, “Wireless information and power transfer: Energy efficiency optimization in OFDMA systems,” IEEE Transactions on Wireless Communications, vol. 12, no. 12, pp. 6352–6370, December 2013. [9] J. Hyungsik and R. Zhang, “Throughput maximization in wireless powered communication networks,” IEEE Transactions on Wireless Commun., vol.13, no.1, pp. 418–428, January 2014. [10] S. Lohani, R. A. Loodaricheh, E. Hossain, and V. K. Bhargava, “Relay-based harvestthen-transmit protocol for uplink cellular networks,” in IEEE Globecom Workshops (GC Workshops), December. 2014, pp. 912–917. [11] Krikidis, Ioannis, “Simultaneous information and energy transfer in large-scale networks with/without relaying,” IEEE Transactions on Commun., vol. 62, no. 3, pp. 900–912, March 2014. [12] A. A. Nasir, X. Zhou, S. Durrani, and R. A. Kennedy, “Relaying protocols for wireless energy harvesting and information processing,” IEEE Transactions on Wireless Communications, vol. 12, no. 7, pp. 3622–3636, July 2013. [13] S. K. Yoon, S. J. Kim, and U. K. Kwon, “Energy relaying in mobile wireless sensor networks,” in Proc. IEEE Consumer Communications and Networking Conference (CCNC), January 2013, pp. 673–676. [14] D. Mishra, S. De, S. Jana et al., “Smart RF energy harvesting communications: challenges and opportunities,”IEEE Communications Magazine., vol. 53, no. 4, pp. 70–78, April 2015. [15] T. Riihonen, S. Werner, and R. Wichman, “Comparison of full-duplex and half-duplex modes with a fixed amplify-and-forward relay,” IEEE Wireless Communications and Networking Conference (WCNC), April 2009, pp. 1–5. 10 Mar 2017 at 08:07:55, .005

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[16] M. Moghaddari and E. Hossain, “Cooperative communications in OFDM and MIMO cellular relay networks: Issues and approaches,” in Cooperative Cellular Wireless Networks, E. Hossain, D. I. Kim, and V. K. Bhargava, Eds. Cambridge: Cambridge University Press, 2011. [17] A. A. Nasir, X. Zhou, S. Durrani, and R. A. Kennedy, “Wireless-powered relays in cooperative communications: Time-switching relaying protocols and throughput analysis,” IEEE Transactions on Communications, vol. 63, no. 5, pp. 1607–1622, May 2015. [18] I. Krikidis, S. Timotheou, and S. Sasaki, “RF energy transfer for cooperative networks: Data relaying or energy harvesting?,” IEEE Communications Letters, vol. 16, no. 11, pp. 1772–1775, November 2012. [19] C. Zhong. H. A. Suraweera, G. Zheng, I. Krikidis, and Z. Zhang, “Wireless information and power transfer with full duplex relaying,” IEEE Transactions on Communications, vol. 62, no. 10, pp. 3447–3461, October 2014. [20] Y. Zeng and R. Zhang, “Full-duplex wireless-powered relay with self-energy recycling,” IEEE Wireless Communications Letters, vol. 4, no. 2, pp. 201–204, April 2015. [21] K. Kaushik, D. Mishra, S. De et al., “Experimental demonstration of multi-hop RF energy transfer,”in Proc. 24th International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), September 2013, pp. 538–542. [22] R. A. Loodaricheh, S. Mallick, and V. K. Bhargava, “Resource allocation for OFDMA systems with selective relaying and energy harvesting,” in Proc. IEEE 80th Vehicular Technology Conference (VTC Fall), September 2014, pp. 1–5. [23] H. W. Kuhn, “The Hungarian method for the assignment problem,” in Naval Research Logistic Quarterly, vol. 2, nos. 1–2, pp. 83–97, March 1955. [24] S. O. Krumke, Integer Programming. Polyhedra and Algorithms, 2006 (available at www.bayanbox.ir/view/7671377560979429366/Integer-Programming-Krumke.pdf). [25] R. A. Loodaricheh, S. Mallick, and V. K. Bhargava,“Energy-efficient resource allocation for OFDMA cellular networks with user cooperation and QoS provisioning,” IEEE Transactions on Wireless Communications vol. 13, no. 11, pp. 6132–6146, November 2014. [26] R. Nabar, F. Kneubuhler, and H. Bolcskei, “Performance limits of amplify-and-forward based fading relay channels,” in Proc. IEEE ICASSP, 2004, pp. 565–568. [27] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge: Cambridge University Press, 2004 (available at http://books.google.ca/books?id=mYm0bLd3fcoC). [28] S. Lohani, R. A. Loodaricheh, E. Hossain, and V. K. Bhargava, “On multiuser resource allocation in relay-based wireless-powered uplink cellular networks,” IEEE Transactions on Wireless Communications, vol. 15, no. 3, pp. 1851–1865, March 2016. [29] A. Sabharwal, P. Schniter, D. Guo et al., “In-band full-duplex wireless: Challenges and opportunities,” IEEE Journal on Selected Areas in Communications, vol. 32, no. 9, pp. 1637–1652, September 2014. [30] H. Ju and R. Zhang, “Optimal resource allocation in full-duplex wireless-powered communication network,” IEEE Transactions on Communications, vol. 62, no. 10, pp. 3528–3540, October 2014. [31] E. Ahmed, A. M. Eltawil, and A. Sabharwal, “Self-interference cancellation with phase noise induced ICI suppression for full-duplex systems,” in Proc. IEEE Global Communications Conference (GLOBECOM), December 2013, pp. 3384–3388. [32] D. Korpi, L. Anttila, V. Syrjala, and M. Valkama, “Widely linear digital self-interference cancellation in direct-conversion full-duplex transceiver,” IEEE Journal on Selected Areas in Communications, vol. 32, no. 9, pp. 1674–1687, September 2014. 10 Mar 2017 at 08:07:55, .005

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[33] X. Zhou, R. Zhang, and C. K. Ho, “Wireless information and power transfer: Architecture design and rate-energy tradeoff,” IEEE Transactions on Communications, vol. 61, no. 11, pp. 4754–4767, November 2013. [34] Y. Gu and S. Aissa, “Interference aided energy harvesting in decode-and-forward relaying systems,” in Proc. IEEE International Conference on Communications (ICC), June 2014, pp. 5378–5382. [35] A. A. Nasir, D. T. Ngo, X. Zhou, R. A. Kennedy, and S. Durrani, “Joint resource optimization for heterogeneous multicell networks with wireless energy harvesting relays,” CoRR, 2014 (available at http://dblp.uni-trier.de/rec/bib/journals/corr/NasirNZKD14). [36] H. Chen, Y. Jiang, Y. Li, Y. Ma, and B. Vucetic, “A game-theoretical model for wireless information and power transfer in relay interference channels,”in Proc. IEEE International Symposium on Information Theory (ISIT), June–July 2014, pp. 1161–1165.

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Multiple Antennas and Beamforming for SWIPT Systems Derrick Wing Kwan Ng, Shiyang Leng, and Robert Schober

5.1

Introduction The development of wireless communication networks worldwide has triggered an exponential growth in the number of wireless communication devices and sensors for applications such as e-health, automated control, environmental monitoring, energy management, and safety management. It is expected that, by 2020, the number of inter-connected devices on the planet may reach 50 billion. Recent efforts in nextgeneration communication system development aim at providing secure, ubiquitous, and high-speed communication with guaranteed quality of service (QoS). However, the related tremendous increase in the number of transmitters and receivers has also led to a huge demand for energy. A relevant technique for reducing the energy consumption of wireless devices is multiple-input multiple-output (MIMO), since it offers extra degrees of freedom for more efficient resource allocation. In particular, multiuser MIMO, where a transmitter equipped with multiple antennas serves multiple single-antenna receivers, is considered an effective solution for realizing the potential performance gains offered by multiple antennas to improve the system spectral efficiency and reduce the transmit power. On the other hand, battery-powered mobile devices such as wireless sensors have been widely deployed and have become critical components of many wireless communication networks over the past decades. However, batteries have limited energy storage capacity and their replacement can be costly or even impossible, which creates a performance bottleneck in wireless networks. As a result, energy harvesting technology is foreseen as a viable solution to remove the last wires of wireless devices. The integration of energy harvesting (EH) capabilities into communication devices facilitates self-sustainability of energy limited communication systems. Solar, wind, hydroelectric, and piezoelectric are the major conventional energy sources for EH. For instance, energy harvesters for harvesting wind and solar energy have been successfully integrated into base station transmitters for providing communication services in remote areas [1]. However, the availability of these natural energy sources is usually limited by location, climate, and time of day. Besides, the implementation of conventional energy harvesters may be problematic and renewable energy from natural sources may not be Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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available in indoor environments. Thus, a new form of controllable energy source for portable wireless devices is needed in order to extend the lifetime of communication networks.

5.1.1

Background In 1899, Nikola Tesla proposed the wireless transmission of electrical power via a magnifying transmitter, an advanced version of the Tesla coil transmitter. The use of wireless power transfer (WPT) avoids the potentially high costs of planning, installing, displacing, and maintaining power cables in buildings and infrastructure. Despite its convenience, one of the major challenges in realizing WPT is its low power transfer efficiency. In practice, wireless power has to be transferred via a carrier signal with a high carrier frequency such that antennas of reasonable size can be used for harvesting power. The associated path loss severely attenuates the signal, leading to only a small amount of power being harvested at the receiver. Besides, the initial efforts on WPT focused on high-power-consumption applications. This raised serious public health concerns about strong electromagnetic radiation which prevented the further development of WPT in the late twentieth century. As a result, this area developed slowly until recent advances in silicon technology and multiple-antenna technology made WPT attractive once again. In particular, the breakthrough in silicon technology has significantly reduced the energy demand of simple wireless devices. Thus, harvesting energy1 from background radiofrequency (RF) signals originating from ambient transmitters can support the power needs of low-power-consumption receivers. Besides, multiple-antenna technology has revolutionized the design of traditional communication systems for a better utilization of limited system resources. For example, a multiple-antenna transmitter can focus its transmitted signal into certain locations to improve the signal reception at the receivers. It has been shown that the use of multiple antennas in communication systems can significantly reduce the total transmit power and improve the system energy efficiency for given QoS requirements. Thus, it is envisioned that multiple-antenna technology is also the key to unlock the potential of WPT.

5.1.2

Literature Survey Radio-frequency signals are an abundant source of energy for EH [2–6]. Nowadays, EH circuits are able to harvest microwatts to milliwatts of power over a range of several meters for a transmit power of 1 W and a carrier frequency of less than 1 GHz [7]. For instance, Intel has demonstrated the wireless charging of a temperature and humidity meter as well as a liquid-crystal display by using the signals radiated by a TV station 4 km away [8]. Thus, RF energy can be a viable energy source for devices with low power consumption, e.g., wireless sensors [4, 5]. There have been some preliminary applications of wireless energy transfer such as wireless body area networks (WBANs) 1 In this chapter, a normalized energy unit, i.e., Joule-per-second, is considered. Therefore, the terms “power”

and “energy” are used interchangeably.

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for biomedical implants, passive radio-frequency identification (RFID) systems, and wireless sensor networks. Moreover, RF EH provides the possibility of simultaneous wireless information and power transfer (SWIPT) since RF signals carry both information and energy. Yet, this new technology introduces a paradigm shift in system and resource allocation algorithm design. In particular, the role of multiple-antenna designs in SWIPT has to be carefully investigated due to the imposed new challenges and QoS requirements on efficient WPT. In the following, we provide a brief literature survey on SWIPT systems. The fundamental tradeoff between wireless power transfer and wireless information was studied in [2] and [3] for flat fading and frequency selective fading, respectively. Specifically, a theoretical optimal receiver was assumed in [2, 3] such that EH and information decoding can be performed simultaneously on the same received signal, which is not implementable in practice yet. As a compromise solution, three different types of receivers, namely power-splitting, separated, and time-switching, were proposed in [9, 10]. In particular, the power-splitting receiver splits the received power into two power streams with a certain power-splitting ratio to facilitate simultaneous EH and information decoding in the same receiver [11–16]. The authors of [9] and [10] investigated the rate–energy tradeoff regions for two-receiver and point-to-point systems, respectively. On the other hand, the authors of [11] focused on the power allocation algorithm design in ergodic fading channels for a point-to-point single-user SWIPT system with a power-splitting receiver. The authors of [12], by taking into account the power consumption in electronic circuitries and RF transmission, proposed different power allocation algorithms and showed that introducing power-splitting receivers can improve the energy efficiency of a communication system. On the other hand, SWIPT raises concerns regarding communication security due to the broadcast nature of wireless channels and the relatively high signal power for SWIPT. As a result, beamformer design for multiple-antenna SWIPT systems with consideration of the physical layer security was studied in [13, 16–18]. The authors of [13] and [16], by taking into account potential eavesdropping by EH receivers, designed beamformers for minimization of the total transmit power for the cases of perfect channel state information (CSI) and imperfect CSI, respectively. A multi-objective framework was adopted in [17] to handle conflicting system design goals for providing communication security while guaranteeing QoS in WPT to EH receivers. In [18], beamforming design was investigated for the maximization of secrecy rate. In [13, 16–18], artificial noise generation and multiple antennas were used to ensure secure SWIPT. Specifically, the artificial noise serves as interference to degrade the channel quality of potential eavesdroppers and acts as an energy source for expediting energy harvesting at the receivers. The aforementioned works in the literature suggest that multiple-antenna systems provide a higher energy transfer efficiency than single-antenna systems. Specifically, multiple-antenna transmitters utilize the spatial degrees of freedom to create directional signal transmission, which is crucial for improving the overall system performance. In the following, we focus on beamforming design for multiple-antenna SWIPT systems and investigate different practical design problems. The remainder of this chapter is organized as follows. In Section 5.2, we describe the adopted system model. 10 Mar 2017 at 08:07:47, .006

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In Sections 5.3 and 5.4, we formulate and solve single-objective and multi-objective optimization problems arising in the design of SWIPT systems, respectively. Section 5.5 studies beamforming design for guaranteeing secure communications in SWIPT systems. In Section 5.6, we discuss some research challenges in multiple-antenna SWIPT systems and paths to potential solutions. Section 5.7 concludes this chapter with a brief summary. Now, we first introduce the main notations adopted in this chapter.

5.1.3

Notation The key mathematical notations are summarized in Table 5.1. We use boldface capital and lower-case letters to denote matrices and vectors, respectively. AH , Tr(A), and Rank(A) represent the Hermitian transpose, the trace, and the rank of matrix A, respectively; A 0 and A  0 indicate that A is a positive definite and a positive semidefinite matrix, respectively; vec(A) denotes the vectorization of matrix A by stacking its columns from left to right to form a column vector; λmax A denotes the maximum eigenvalue of Hermitian matrix A; IN is the N × N identity matrix; CN×M and RN×M denote the set of all N × M matrices with complex and real entries, respectively; HN denotes the set of all N × N Hermitian matrices; diag(x1 , . . . , xK ) denotes a diagonal matrix with the diagonal elements given by {x1 , . . . , xK }; |·| and · denote the absolute value of a complex scalar and the l2 -norm of a vector, respectively; the circularly symmetric complex Gaussian (CSCG) distribution is denoted by CN (μ, σ 2 ) with mean μ and variance σ 2 ; ∼ stands  for “distributed as”; 1 denotes a column vector with all elements equal to one. · a,b returns the (a, b)th element of the input matrix, θ n is the     nth unit column vector, i.e., θ n t,1 = 1, if t = n, and θ n t,1 = 0, ∀t = n. Table 5.1. Nomenclature adopted in this chapter Notation

Description

h gj w wE v 2 , σ2 σant s ρ req NT RTol ER ξ ηIR ηEH Pmax Pmaxn Pant Pc Pminj

Channel vector between the transmitter and the information receiver Channel vector between the transmitter and energy receiver j Information beamforming vector Energy signal vector Artificial noise vector Antenna and signal processing noise power Power splitting ratio Minimum required signal-to-noise-plus-interference ratio Number of transmit antennas Maximum tolerable data rate Power amplifier efficiency Information rate energy efficiency Energy transfer energy efficiency Maximum transmit power of the transmitter Maximum transmit power of antenna n Antenna power consumption Baseband signal processing circuit power consumption Minimum required power transfer to receiver j

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Figure 5.1 A multiuser SWIPT downlink model with an information receiver (IR) and J = 2 idle

receivers. The idle receivers work as energy harvesting receivers (ERs) to harvest energy from the received radio-frequency (RF) signals for extending their lifetimes.

5.2

System Model We consider a downlink SWIPT system which consists of a transmitter, one information receiver (IR), and J energy harvesting receivers (ERs). The transmitter is equipped with NT transmit antennas while the receivers are single-antenna devices, see Figure 5.1. The transmission is divided into time slots. In each time slot, the transmitter conveys information to a given receiver and transfers energy to all receivers. The downlink received signals at the IR and energy harvesting receiver j are given by, respectively, y = hH x + za , yER j

=

gH j x + zj ,

(5.1) ∀j ∈ {1, . . . , J},

(5.2)

where x ∈ CNT ×1 denotes the transmitted symbol vector. hH ∈ C1×NT is the channel 1×NT is the channel vector between the transmitter and the desired receiver and gH j ∈ C vector between the transmitter and idle receiver j. We note that both variables, h and gj , include the effects of the multi-path fading and path loss of the associated channels. za and zj are additive white Gaussian noises (AWGNs) resulting from the receive antenna 2 and σ 2 , respectively. at the IR and ER j, respectively, with zero mean and variance σant antj This simple system model is adopted for illustration of the beamforming design in multiple-antenna SWIPT systems in Sections 5.3 and 5.4 in this chapter.

5.3

Single-Objective Optimization The design of a single-objective utility-based resource allocation algorithm is the key for optimal utilization of the physical layer resources. In particular, different resource 10 Mar 2017 at 08:07:47, .006

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allocation algorithm designs have been studied in the literature for different wireless communication systems [19–24]. Specifically, the use of limited physical layer resources such as bandwidth, energy, time, and space is optimized for achieving different system design goals such as maximum spectral efficiency and power efficiency. In practice, by exploiting the extra degrees of freedom offered by multiple antennas, information/energy beamforming can be effectively performed when the channel state information (CSI) of the receivers is available at the transmitter. There are two main approaches for downlink CSI acquisition. In frequency division duplex (FDD) systems, the CSI can be acquired by feeding back the CSI from the receivers to the transmitter. On the other hand, in time division duplex (TDD) systems, the CSI can be obtained by exploiting the channel reciprocity between the uplink and downlink channels. In particular, the downlink CSI of the transmitter to the receivers can be estimated by measuring the uplink training sequences embedded in handshaking signals. In addition to the conventional QoS requirements such as throughput, energy efficiency, fairness, and delay, the efficient transfer of energy plays an important role as a new QoS requirement in SWIPT systems. It is expected that new resource allocation algorithm designs will be needed to satisfy this requirement. For instance, one possible design goal is the optimization of the covariance matrix of the transmit signal for achievable rate maximization of an IR subject with respect to a minimum required amount of energy transferred to the ERs. In the following, we first study different beamformer designs for achieving different system objectives by assuming that perfect CSI is available at the transmitter.

5.3.1

Energy Beamforming In this section, we focus on beamformer design to facilitate efficient wireless power transfer (WPT) from the transmitter to the receivers. In particular, we adopt random signals as energy carriers and the transmitter chooses the transmit signal vector x as x=

, ws !"# random signal

(5.3)

where s ∈ C1×1 and w ∈ CNT ×1 are the pseudo-random transmit signal and the corresponding beamforming vector. We assume without loss of generality that E{|s|2 } = 1. In practice, random energy signals may be preferable insofar as they spread the signal power evenly over the operating bandwidth and avoid the power spikes typical of deterministic sinusoidal carrier signals. Different hardware circuitries [25, 26] are available for harvesting energy from the RF. The associated system models and the corresponding energy harvesting efficiencies can be significantly different. Therefore, we do not assume a particular type of energy harvesting circuit, and hence the following discussion of beamformer design is isolated from the specific hardware implementation details. The total harvested RF power at ER j is modeled as 10 Mar 2017 at 08:07:47, .006

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2 Qj = ηj E{|gH j x| } 2 = ηj |gH j w| H = ηj Tr(gH j ww gj ),

(5.4)

where 0 ≤ ηj ≤ 1 is a constant that accounts for the RF-to-electrical energy conversion efficiency. Now, we examine the optimal transmit covariance matrix, W = wwH , for maximization of the total power transfer. The optimal transmit covariance matrix design can be formulated as the following optimization problem. Problem 1.

Total harvested power maximization: maximize Tr(WG) W∈HNT

subject to

Tr(W) ≤ Pmax ,

W  0,

(5.5)

where Pmax is the maximum transmit power budget for the transmitter and G = J H j=1 ηj gj gj is the equivalent channel between the transmitter and the J ERs. Let R = min{NT , J} and let the singular value decomposition of G be given by G = U 1/2 VH , where  = diag(g1 , g2 , . . . , gR ) with g1 ≥ g2 ≥ . . . ≥ gR . U ∈ CJ×R and V ∈ CJ×R are two matrices with orthonormal columns. Besides that, we denote v1 as the first column of V. Then, we introduce the following proposition for revealing the solution of Problem 1. proposition 5.1. [27] The optimal solution for Problem 1 is given by W = Pmax v1 vH 1. In other words, the maximum total harvested power can be achieved by beamforming. In particular, the energy beam, w, aligns with the direction of the strongest eigenmode of the matrix GGH . This transmission strategy is known as energy beamforming in the literature [27]. Up to now, we have studied only WPT to the receivers without considering the possibility of concurrent wireless information transfer. In fact, practical receivers for information decoding cannot be used to harvest energy from the same RF signals due to the different nature of the signal processing and receiver sensitivities required [26]. In other words, the received RF signal exploited for energy harvesting cannot be reused for information decoding, and vice versa. As a result, a special receiver structure is required in order to enable SWIPT. In the next section, we focus on two commonly used receiver architectures, namely, “separated receivers” and “power splitting receivers,” both of which facilitate SWIPT. Also, we develop corresponding beamforming designs for better utilization of the limited system resources.

5.3.2

SWIPT: Separated Receivers In a separated receiver architecture, an EH circuit and an ID circuit are implemented as two separate receivers, which are served by a common multiple-antenna transmitter 10 Mar 2017 at 08:07:47, .006

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[26–39]. Separated receivers can be easily implemented by using off-the-shelf components for the two individual receivers. On the other hand, the transmitter chooses the transmit signal vector x as x=

, ws !"# beamformed information signal

(5.6)

where s ∈ C1×1 now represents the information-bearing signal. As in the case of WPT,   2 we assume without loss of generality that E |s| = 1.

5.3.2.1

Beamforming Design In this section, we focus on beamforming design for maximization of the system achievable rate, which can be formulated as the following optimization problem.

Problem 2.

Achievable rate maximization:   Tr(WH) maximize log2 1 + 2 σant + σs2 W∈HNT subject to C1 : Tr(WG) ≥ Pmin , C2 : Tr(W) ≤ Pmax ,

(5.7)

where H = hhH , Pmin in constraint C1 is the minimum required total system power transfer, and σs2 is the signal processing noise at the receiver, which is modeled as AWGN. The optimal transmit covariance matrix is given by [27]   2 + σ2 1 σant s ∗ −1 − (5.8) hH B−1 , W =B h B−1 h2 B−1 h4 where B = μ∗ IT − λ∗ G. Here, λ∗ and μ∗ are the optimal dual variables which can be found by the gradient method or the ellipsoid method for satisfying constraints C1 and C2 , respectively. It can be observed from (5.8) that the optimal covariance is a rankone matrix, i.e., Rank(W) = 1. In other words, beamforming is the optimal strategy to maximize the achievable rate while guaranteeing a minimum required total system power transfer. Specifically, the transmit beamforming direction should align with the vector B−1 h which represents the equivalent channel spanned jointly by the channels of the IR and the ERs.

5.3.2.2

Numerical Example In this section, we present a numerical example to illustrate the benefits of multiple transmit antennas and multiple ERs for SWIPT. The most important simulation parameters are listed in Table 5.2 and the maximum transmit power Pmax is set to 30 dBm. We assume that all the receivers are located 10 meters away from the transmitter. 10 Mar 2017 at 08:07:47, .006

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Table 5.2. System parameters Parameter

Value

Carrier center frequency Path-loss exponent Path-loss model Multi-path fading distribution Rician factor Transmit and receive antenna gain Noise variance, σs2 2 Antenna noise variance, σant System bandwidth RF-to-electrical energy conversion efficiency, ηj

915 MHz 2 TGn Model A [40] Rician fading 6 dB 10 dBi and 0 dBi −23 dBm −114 dBm 200 kHz 0.5

Average achievable rate (bit/s/Hz)

178

6.6

Harvested power gain due to extra ERs

6.4 6.2 6

Achievable rate gain due to extra N T N T = 4, J = 2

5.8

N T = 4, J = 4 5.6 5.4 200

N T = 8, J = 2 N T = 8, J = 4 300

700 800 400 500 600 Average total harvested power (mW)

800

Figure 5.2 Average achievable rate (bit/s/Hz) versus the average total harvested power (μW) for

one IR, different numbers of ERs, J, and different numbers of transmit antennas, NT .

Figure 5.2 depicts an example of beamforming in SWIPT systems. We show the average system achievable rate versus the average total harvested energy in a downlink system for the optimal beamforming scheme. In particular, a transmitter equipped with NT antennas serves one single-antenna IR and J single-antenna ERs. As can be observed, with the optimal beamformer, the tradeoff region of the system achievable rate and the harvested energy increases significantly with NT . This due to the fact that the extra degrees of freedom offered by multiple transmit antennas help the transmitter to focus its energy and thus improve the beamforming efficiency. Besides, the average total system harvested energy improves with the number of ERs as more receivers participate in energy harvesting. In the next section, we focus on the general case where the IR wants to decode the modulated information and harvest energy from the received signal. 10 Mar 2017 at 08:07:47, .006

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Signal processing noise ss2

Information and power transfer Power amplifier

Antenna noise Power-splitting ratio = r s 2ant

Transmitter signal Processing core

179

Power-splitting ratio =

1–r

Power-splitting unit

Receiver signal processing core Rechargeable Battery Energy harvesting circuit

Power-splitting receiver

Figure 5.3 The block diagram of the transceiver model for wireless information and power

transfer with a power-splitting receiver.

5.3.3

SWIPT: Power-Splitting Receivers In this section, we consider power-splitting receivers [11–16], which split the received signal into two power streams with power-splitting fractions 1 − ρ and ρ, see Figure 5.3, for harvesting energy and decoding the modulated information, respectively. Specifically, the power-splitting unit is installed in the analog front-end of the receiver and is assumed to be a perfect passive analog device; it does not introduce any extra power gain, i.e., 0 ≤ ρ ≤ 1, and does not add noise to the received signal. Indeed, the power-splitting receiver architecture is a generalization of traditional information receivers (IRs) and energy receivers (ERs). In fact, on imposing power splitting fractions of ρ = 1 and ρ = 0, the power-splitting receiver reduces to a traditional IR and ER, respectively. Hence, the separated receiver studied in the previous section is a special case of a power-splitting receiver.

5.3.3.1

System Optimization In the following, we study the power-efficient resource allocation design for SWIPT networks. We assume that there is one power-splitting receiver and J pure ERs in the system. The power-efficient system optimization can be formulated as the following total transmit power minimization problem.

Problem 3.

Total transmit power minimization: minimize w2 w,ρ

subject to

C1 :

ρ|hH w|2 2 + σ2 ρσant s

≥ req ,

2 2 C2 : (1 − ρ)η|gH j w| + (1 − ρ)ησant ≥ Pmin , 2 2 C3 : ηj |gH j w| + ηj σant ≥ Pminj , ∀j ∈ {1, . . . , J}, $ % ≤ Pmaxn , ∀n ∈ {1, . . . , NT }, C4 : wwH n,n

C5 : 0 ≤ ρ ≤ 1,

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(5.9)

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where the variable req in C1 specifies the minimum requirement on the signalto-noise ratio (SNR) of the receiver for information decoding. η in C2 denotes the RF-to-electrical energy conversion efficiency for IR. Pmin and Pminj in C2 and C3 are the minimum required power transfer to the power-splitting IR and ER j, respectively. In C4 , Pmaxn denotes the maximum transmit power from antenna n, since each antenna is powered by an individual power amplifier. C5 is the boundary constraint for the power-splitting variable ρ. The problem in (5.9) is a non-convex optimization problem. In particular, constraints C1 –C3 are non-convex, which does not facilitate the design of a computationally efficient beamformer. In order to design a tractable beamfomer, we first rewrite (5.9) in an equivalent2 form: minimize Tr(W) W∈HNT ,ρ

 2 σ 2 + s , subject to C1 : Tr(HW) ≥ req σant ρ Pmin 2 ≥ , C2 : Tr(HW) + σant (1 − ρ)η Pminj 2 C3 : Tr(Gj W) + σant ≥ , ∀j ∈ {1, . . . , J}, ηj   C4 : Tr  n W ≤ Pmaxn , ∀n ∈ {1, . . . , NT }, 

C5 : 0 ≤ ρ ≤ 1, C6 : W  0, C7 : Rank(W) ≤ 1,

(5.10)

where Gj = gj gH j . We note that the per-antenna transmit power in constraint C4 in NT ×1 is the nth (5.10) can be represented as Tr( n W), where  n = θ n θ H n and θ n ∈ R unit vector of length NT defined in the notation section. Now, the only non-convexity in problem (5.10) is due to constraint C7 . In particular, constraint C7 is a combinatorial constraint that requires a brute force search for finding a global optimal solution. To circumvent the non-convexity, we adopt a semidefinite programming (SDP) relaxation to (5.10) by relaxing constraint C7 : Rank(W) = 1, i.e., removing it from the problem formulation, which leads to the following problem. Problem 4.

SDP relaxation of Problem 3: minimize Tr(W) W∈HNT ,ρ

subject to C1 –C6 ,

( Rank(W) ≤ 1. C7 : ( ((((

(5.11)

2 In this chapter, “equivalent” means that two problem formulations share the same optimal solution.

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Problem 4 is a convex SDP that can be solved efficiently by standard numerical solvers for convex programs such as SeDuMi [41] and SDPT3 [42]. From the basic principles of optimization theory, if the obtained solution W for the relaxed problem admits a rank-one matrix, then it is the optimal solution of the original problem in (5.10). Then, the optimal w can be obtained by performing an eigenvalue decomposition of W. However, in general, the constraint relaxation may not be tight since it is possible that Rank(W) > 1. In the following, we reveal the tightness of the adopted SDP relaxation in (5.11) via examination of the dual problem and the Karush–Kuhn–Tucker (KKT) conditions of (5.11). To this end, we need the Lagrangian function of (5.11), which is given by L(W, ρ, α, β, φ, γ , δ, θ , Y)

   σ2 2 + s = Tr(W) − Tr(YW) + α − Tr(HW) + req σant ρ   Pmin 2 + + β − Tr(HW) − σant (1 − ρ)η   J  Pminj 2 + φj − Tr(Gj W) − σant + ηj j=1

+

NT 

    γn Tr  n W − Pmaxn − δρ + θ (ρ − 1).

(5.12)

n=1

Here, α ≥ 0 is the dual variable for the minimum required signal-to-interferenceplus-noise ratio (SINR) of the hybrid receiver in C1 . φ is the vector of dual variables of the requirement for a minimum transferred power in C3 with elements φj ≥ 0, j ∈ {1, . . . , J}. The dual variable β ≥ 0 corresponds to the minimum required power transfer to the desired receiver in C2 . γ , with elements γn ≥ 0, n ∈ {1, . . . , NT }, is the dual variable vector associated with the per-antenna maximum transmit power constraint in C4 . δ, θ ≥ 0 are the dual variables for the boundary constraints of optimization variable ρ in C5 . The matrix Y  0 is the dual variable for the semidefiniteness constraint on matrix W. Thus, the dual problem for the SDP relaxed problem is given by maximize

α,β,φ,γ ,δ,θ≥0, Y0

minimize W∈HNT ,ρ

L(W, ρ, α, β, φ, γ , δ, θ, Y).

(5.13)

Now, we reveal the tightness of the SDP relaxation adopted in (5.11) in the following theorem. theorem 5.1. Assuming that the channel vectors of the IR, h, and the ERs, gj , j ∈ {1, . . . , J}, can be modeled as statistically independent random variables, the solution of (5.11) is rank-one, i.e., Rank(W) = 1, with probability one. Proof. Please refer to Section 5.8.1. 10 Mar 2017 at 08:07:47, .006

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In other words, the SDP relaxation is tight whenever the channels satisfy the condition stated in Theorem 5.1. Besides, the optimal beamformer for (5.9), w∗ , can be obtained with probability one by performing an eigenvalue decomposition of the solution W of (5.11) and selecting the principal eigenvector as the beamformer.

Numerical Examples In this section, we evaluate the system performance of the proposed beamformer design via simulations. The simulation parameters adopted are listed in Table 5.2. In particular, we assume that there are one-power splitting IR and J = 3 ERs, and that they are located 10 m away from the transmitter. The maximum transmit power per antenna is set to Pmaxn = 30 dBm, ∀n ∈ {1, . . . , NT }, and ηj = η = 0.5. The average total transmit power of the transmitter is obtained by averaging over different multi-path fading realizations.

Average Total Transmit Power Figure 5.4 depicts the average total transmit power versus the minimum required SNR of the power splitting receiver, req , for different resource allocation schemes. It can be observed that the average total transmit power of the proposed scheme is a monotonically increasing function of req . This is due to the fact that a higher transmit power is required for satisfying constraint C1 when the requirement on req becomes more stringent. Besides, the total transmit power decreases with increasing number of transmit antennas NT . The extra degrees of freedom offered by the multiple transmit antennas help in focusing energy on the power-splitting receiver, which improves the power efficiency of the system. Furthermore, we compare our optimal resource

36 Average total transmit power (dBm)

5.3.3.2

Baseline scheme N T = 8, optimal scheme N T = 8, baseline scheme N T = 10, optimal scheme N T = 10, baseline scheme N T = 12, optimal scheme N T = 12, baseline scheme

34 32 30 28 26

Opitmal scheme

24 22 20 18 6

8

10 12 14 16 18 20 Minimum requried SNR (dB)

22

24

Figure 5.4 Average total transmit power (dBm) versus the minimum required SNR of the

power-splitting receiver, req (dB), for different resource allocation schemes and different numbers of transmit antennas, NT . 10 Mar 2017 at 08:07:47, .006

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allocation scheme with a baseline scheme. Specifically, a fixed power-splitting ratio of ρ = 0.5 and maximum ratio transmission (MRT) are adopted in the baseline scheme for delivering the information signal to the power-splitting receiver. Then, we optimize the power allocated to the MRT beamforming matrix W for the minimization of the total transmit power subject to the same constraints as in (5.11). We note that, although the MRT matrix is a rank-one matrix, the solution obtained is generally a suboptimal solution with respect to (5.9). It can be observed that the proposed optimal scheme has a superior performance, i.e., a lower total transmit power, to the baseline scheme. In particular, a 3 dB power saving is achieved with the optimal scheme compared with the baseline scheme in the high-SNR regime, because of the proposed optimization framework.

Average Power-Splitting Ratio It can be observed from Figure 5.5 that the average power-splitting ratio increases with the required SNR, req . As the SNR requirement becomes more stringent, the powersplitting receiver is forced to use more of the received signal power for information decoding at the power-splitting receiver to improve the receive SNR. In other words, adopting a fixed power-splitting ratio, e.g. baseline scheme, is strictly suboptimal for reducing the total transmit power in general. On the other hand, it is expected that the number of transmit antennas does not have a large impact on the value of the power-splitting ratio. This is because, for a fixed receive SNR requirement at the powersplitting receiver, the transmitter has to maintain the same level of receive signal strength at the power-splitting receiver regardless of the number of transmit antennas. In fact, the extra degrees of freedom offered by the increased number of transmit antennas are 1 NT = 8 NT = 10 NT = 12

Average power-splitting ratio r

0.9 0.8 0.7 0.6 0.5 0.4 0.5 0.2 0.1 0

6

9

12 15 18 21 Minimum requried SNR (dB)

24

Figure 5.5 Average power-splitting ratio versus the minimum required SNR of the

power-splitting receiver, req (dB), for the proposed optimal resource allocation scheme. The groups of bars from left to right represent NT = 8, 10, 12, respectively. 10 Mar 2017 at 08:07:47, .006

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Average total harvested power (mW)

Average total harvested power at power-splitting receiver 600 Optimal scheme, NT = 8 Baseline scheme, NT = 8 400

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Optimal scheme, NT = 8 Baseline scheme, NT = 8

600

Minimum required power transfer 400 200 0

6

9

12

15

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Minimum requried SNR (dB) Figure 5.6 Average total harvested power at the power-splitting receiver and per ER, versus the

minimum required SNR of req (dB). Each group of bars from left to right represents the proposed optimal resource allocation scheme and the baseline scheme, respectively.

exploited to reduce the transmit power, but not to increase the receive SNR at the powersplitting receiver.

Average Total Harvested Power Figure 5.6 shows the average total harvested power versus the minimum required SNR of the power-splitting receiver, req , for different resource allocation schemes and NT = 8. It can be seen from the upper half of Figure 5.6 that the proposed optimal resource allocation scheme always satisfies the minimum required power transfer constraint C2 with equality, despite the increasing required SNR, which confirms the observation from the KKT conditions in Section 5.8.1. In contrast, for the baseline scheme, an exceedingly large amount of power is transferred to the power-splitting receiver which leads to an unnecessarily large transmit power, see Figure 5.4. On the other hand, it can be observed from the lower half of Figure 5.6 that the total average power harvested per ER increases with req . In fact, the transmitter has to allocate more power to the information-bearing signal to achieve a larger req . As a result, more power is available in the RF and can be harvested by the ERs. 10 Mar 2017 at 08:07:47, .006

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Average total transmit power (dBm)

34 32 30 28 26 24

NT = 8, optimal scheme NT = 8, baseline scheme NT = 10, optimal scheme NT = 10, baseline scheme NT = 12, optimal scheme NT = 12, baseline scheme

22 20 18

50 250 300 100 150 200 Minimum required power transfer Pmin (mW) Figure 5.7 Average total transmit power (dBm) versus the minimum required power transfer per

receiver, Pmin (μW), for different resource allocation schemes and different numbers of transmit antennas, NT .

Average Total Transmit Power versus Pmin Figure 5.7 shows the average total transmit power versus the minimum required power transfer to the receivers, Pmin , for different resource allocation schemes. We assume that both the IR and the ERs require the same minimum amount of power transfer, i.e., Pmin = Pminj , ∀j ∈ {1, . . . , J}. The minimum required SNR of the power-splitting receiver is set to req = 6 dB. It is expected that the total transmit power increases with the minimum required power transfer. In fact, as the minimum required power transfer becomes more stringent, the feasible solution set shrinks, which reduces the flexibility of the optimal beamforming. On the other hand, the average total transmit power decreases with increasing number of transmit antennas. The extra degrees of freedom offered by the multiple transmit antennas facilitate a more power-efficient resource allocation. Besides, the proposed optimal scheme provides a substantial power saving compared with the baseline scheme owing to the optimization adopted.

5.3.4

Robust Beamforming In the last section, perfect CSI of all receivers is assumed to be available at the transmitter for beamformer design. In practice, the IR performs handshaking with the transmitter at the beginning of each scheduling slot. Besides, the IR is required to send positive acknowledgement (ACK) packets to inform the transmitter of successful reception of the information packets. Hence, the transmitter is able to track and update the CSI estimate of the IR frequently, on the basis of training sequences or feedback information in handshaking signals and ACK packets. Therefore, perfect CSI for the transmitter-toIR link, i.e., h, can be assumed to be available during the entire transmission period. 10 Mar 2017 at 08:07:47, .006

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However, the ERs are idle and there is no interaction between them and the transmitter after handshaking. As a result, the CSI of the ERs becomes outdated during transmission, which should be taken into account for the design of beamformers. To capture the impact of the CSI imperfection for the beamformer design, we adopt a deterministic model [43–46] for modeling the CSI uncertainty. In particular, the CSI of the link between the transmitter and ER j is modeled as gj = gˆ j + gj , ∀j ∈ {1, . . . , J},   2 j  gj ∈ CNT ×1 : gH j gj ≤ εj , ∀j,

(5.14) (5.15)

where gˆ j ∈ CNT ×1 is the CSI estimate available at the transmitter at the beginning of a scheduling slot and gj represents the unknown channel uncertainty due to the time-varying nature of the channel during transmission. The continuous set j in (5.15) defines a Euclidean sphere and contains all possible channel uncertainties. Specifically, the radius εj represents the size of the sphere and defines the uncertainty region of the CSI of ER j. remark 1. In practice, the value of εj2 depends on the coherence time of the associated channel, the channel estimation method adopted, and the duration of transmission.

5.3.4.1

Beamforming for Robust and Power-Efficient SWIPT In this section, we consider beamformer design for separated receivers when the CSI imperfectness of the ERs is taken into account. The algorithm design is formulated as the following optimization problem.

Problem 5.

Robust beamforming:

minimize w2 w

wH Hw ≥ req , 2 + σ2 σant s $ % C2 : wwH ≤ Pmaxn , ∀n ∈ {1, . . . , NT },

subject to C1 :

n,n

2 C3 : min ηj |gH j w| ≥ Pminj , ∀j ∈ {1, . . . , J}. gj ∈j

(5.16)

This problem formulation aims at minimizing the transmit power while guaranteeing a minimum required power transfer to ER j, assuming that the estimation error gj is in the set j . Problem 5 is a non-convex optimization problem. In particular, constraint C1 and constraint C3 span a non-convex feasible solution set, which is an obstacle in designing computationally efficient beamformers. In order to obtain a tractable result, we re-write Problem 5 in equivalent form as 10 Mar 2017 at 08:07:47, .006

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minimize Tr(W) W∈HNT

Tr(HW) ≥ req , 2 + σ2 σant s   C2 : Tr  n W ≤ Pmaxn , ∀n ∈ {1, . . . , NT },

subject to C1 :

C3 : min ηj Tr(WGj ) ≥ Pminj , ∀j ∈ {1, . . . , J}, gj ∈j

C4: Rank(W) ≤ 1.

(5.17)

We note that constraint C4 is non-convex with respect to the optimization variables. Although constraint C3 is a convex constraint, it represents semi-infinite constraints that are generally intractable for beamforming design. To facilitate the solution, we transform constraint C3 into linear matrix inequalities (LMIs) using the following lemma. lemma 1 (S-Procedure [47]). Let a function fm (x), m ∈ {1, 2}, x ∈ CN×1 , be defined as fm (x) = xH Am x + 2 Re{bH m x} + cm ,

(5.18)

where Am ∈ HN , bm ∈ CN×1 , and cm ∈ R. Then, the implication f1 (x) ≤ 0 ⇒ f2 (x) ≤ 0 holds if and only if there exists a δ ≥ 0 such that ' & ' & A b2 A b1 − H2  0, (5.19) δ H1 b1 c1 b2 c2 provided that there exists a point xˆ such that fk (ˆx) < 0. Now, we apply Lemma 1 to constraint C3 . In particular, we substitute gj = gˆ j + gj into constraint C3 . Therefore, the implication,     H 2 H H H ˆ ˆ gj gj ≤ εj ⇒ C3 :0 ≥ − max gj W gj + 2 Re gj W gj + gj Wˆgj gj ∈j

+

Pminj ηj

, ∀j,

(5.20)

holds if and only if there exists a δj ≥ 0 such that the following LMI constraint holds: ( ) Wˆgj δj INT C3 :SC3j (W, δj ) = H gj gˆ j W −δj εj2 − Pminj /ηj + gˆ H j Wˆ ( ) 0 δk INT = (5.21) + UH gj WUgj  0, ∀j, 0 −δj εj2 − Pminj /ηj $ % for δj ≥ 0, j ∈ {1, . . . , J}, where Ugj = INT gˆ j . Then, we adopt SDP relaxation to handle the non-convexity originating from constraint C4 and the SDP relaxation problem is given as follows. 10 Mar 2017 at 08:07:47, .006

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Problem 6.

Robust beamforming – SDP relaxation: minimize Tr(W) W∈HNT ,δj

Tr(HW) ≥ req , 2 + σ2 σant s   C2 : Tr  n W ≤ Pmaxn , ∀n ∈ {1, . . . , NT },

subject to C1 :

C3 : SC3j (W, δj )  0, ∀j ∈ {1, . . . , J}, ( Rank(W) ≤ 1. C4 : ( ((((

(5.22)

Problem 6 is a convex SDP that can be solved by standard convex numerical solvers [48] via interior point methods. Furthermore, by following a similar approach to that in the proof of Theorem 5.1, it can be proved that the SDP relaxation is tight when h and the ERs, gj , j ∈ {1, . . . , J}, can be modeled as statistically independent random variables. In other words, the SDP relaxation is tight and the optimal solution for Problem 5 can be obtained in polynomial time.

5.3.5

Numerical Examples In this section, we study the performance of the proposed robust beamforming scheme. The simulation parameters adopted are listed in Table 5.2. Besides that, the normalized 2 = ε 2 /g 2 = 0.1, ∀j. The maximum channel estimation error of ER j is given by σER j j j maximum transmit power per antenna is set to Pmaxn = 30 dBm, ∀n ∈ {1, . . . , NT }.

Average Total Transmit Power Figure 5.8 illustrates the average total transmit power versus the minimum required power transfer Pmin for different beamforming schemes and different numbers of transmit antennas. It can be seen that the average total transmit power of the proposed robust scheme increases monotonically with Pmin . In fact, the transmitter is forced to transmit a higher power in order to satisfy the more stringent required Pmin whenever some of the ERs are experiencing bad channel conditions. For comparison, we also show the performance of a benchmark scheme and a naive scheme. For the benchmark scheme, we perform optimal beamforming with perfect CSI, which yields the minimum transmit power required for satisfying constraints C1 –C3 . The naive scheme treats imperfect CSI as if it were perfect CSI and performs the same optimization as the benchmark scheme. It can be observed that a higher transmit power is required for the optimal robust scheme than for the benchmark scheme due to the imperfectness of the CSI. Besides, although the average total transmit power of the naive scheme is smaller than that of the proposed robust scheme, the naive scheme is unable to satisfy the minimum required power transfer at all time instants, which is undesirable in practice, see Figure 5.9. 10 Mar 2017 at 08:07:47, .006

Average total transmit power (dBm)

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Robust scheme, NT = 6 Benchmark scheme, NT = 6 Naive scheme, NT = 6 Robust scheme, NT = 8 Benchmark scheme, NT = 8 Naive scheme, NT = 8

30 28 26

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Robust scheme

24 22 20 18 16 5 10 15 20 25 30 35 Minimum required power transfer Pmin (mW)

Figure 5.8 Average total transmit power (dBm) versus the minimum required power transfer

per receiver, Pmin (μW), for different beamforming schemes and different numbers of transmit antennas, NT . 0.9

QoS outage probability

0.8 0.7 0.6 0.5 0.4 0.3

Naive scheme, N T = 8 Naive scheme, N T = 6 Benchmark scheme, N T = 6, 8 Robust scheme, N T = 6, 8

0.2 0.1 0

5

10 15 20 25 30 35 Minimum required power transfer Pmin (mW)

Figure 5.9 QoS outage probability versus the minimum required power transfer per receiver,

Pmin (μW), for different beamforming schemes and different numbers of transmit antennas, NT .

QoS Outage Probability Figure 5.9 depicts the QoS outage probability versus the minimum required power transfer per receiver for different beamforming schemes and different numbers of transmit antennas, NT . A QoS outage event occurs whenever the beamforming scheme cannot fulfill the QoS requirement for the minimum power transfer in C3 . It can be seen that both the benchmark scheme and the proposed robust scheme achieve zero outage 10 Mar 2017 at 08:07:47, .006

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probability. In other words, the proposed robust scheme is able to guarantee the minimum required power transfer in the scenarios considered, despite the imperfectness of the CSI. However, the outage probability of the naive scheme increases dramatically as Pmin increases, due to the non-robust beamformer design.

5.4

Multi-Objective SWIPT Optimization In the above sections, we studied optimization for SWIPT systems by solving different conventional single-objective optimization problems. However, in practice, multiple conflicting system design, objectives arise naturally in system design, and applying the solutions of single-objective optimization to multi-objective optimization problems (MOOPs) may not lead to satisfactory system performance. Therefore, the concept of multi-objective optimization (MOO) or vector optimization is discussed in this section to provide a systematic procedure for handling conflicting objective functions.3 First, we introduce the MOOP in its standard form as follows. Problem 7. Multi-objective optimization: $ % minimize f(x) = f1 (x), f2 (x), . . . , fK (x) x

subject to gl (x) ≤ 0, l ∈ {1, . . . , L}, hn (x) = 0, n ∈ {1, . . . , N},

(5.23)

where K, L, and N are the numbers of objective functions, inequality constraints, and equality constraints, respectively. x is the vector of optimization variables, fk (x), ∀k ∈ {1, . . . , K}, is the kth objective function,4 gl (x) is the lth inequality constraint, and hn (x) is the nth equality constraint.

5.4.1

Optimization Solution In contrast to single-objective optimization, a solution to a MOOP is more of an abstract concept than a fixed point. In general, there is no single global solution that optimizes all the objective functions simultaneously. Typically, it is necessary to determine a set of points that fit a predetermined definition of an optimum. To this end, we introduce the concept of Pareto optimality for MOOP. definition 5.1 (Pareto optimal). A point, x∗ ∈ F, is Pareto optimal if and only if (iff) there does not exist another point, x ∈ F, such that f(x) ≤ f(x∗ ) and fk (x) < fk (x∗ ) for at least one function. 3 MOO has been applied extensively in the fields of engineering and economics for handling conflicting

design objectives [17, 32, 49, 50]. 4 We note that, in contrast to conventional heuristic approaches where some objectives are converted into

constraints, MOO enables a more rigorous and more flexible system design.

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The Pareto optimal set consists of the attainable operating points that cannot be neglected if the system designer has no preference for a particular system objective. In particular, none of the objectives can be improved without degrading other objectives. Evidently, any point that is not in the Pareto optimal set is strictly suboptimal because there exist other operating points that are better or at least as good with respect to every objective. The Pareto optimal set is an analogy to global optimality that can be achieved in multi-objective optimization. We note that single-objective optimization problems are special cases of MOOPs with K = 1. In other words, if an algorithm can solve the MOOP, then it can be used to solve the corresponding single-objective optimization problem.

5.4.1.1

MOOP Scalarization A common approach to handle MOOPs in practice is the “a-priori method.” This method allows the system designer to specify preferences that may correspond to certain design goals or the relative importance of different objectives. In particular, the system designer adopts a function that produces a scalar describing the preference of the objectives. The function scalarizes the multi-objective function which describes a certain subjective tradeoff between the objectives and thus imposes an order on the objective function vectors in the objective set f(x). There are many scalarization methods in the literature [17, 49, 50]. Here, we introduce the weighted Chebyshev formulation, also known as the weighted max–min formulation, which plays a key role in capturing the Pareto optimal set. The weighted Chebyshev objective function is given by    fChebyshev (x) = max wk fk (x) − fk∗ (x) , (5.24) 1≤k≤K

where fk∗ (x) is the optimal value of the kth objective function and 0 ≤ wk ≤ 1 is a  constant weight factor on objective function k such that K k=1 wk = 1. In fact, the multi-objective problem in (5.24) can provide the complete Pareto optimal set [17] on varying the weights, even if the MOOP is non-convex.

5.4.2

Multi-Objective Optimization for SWIPT In this section, we study multi-objective optimization in SWIPT systems with separated receivers. Recently, driven by environmental concerns, energy efficiency (EE) has become an important metric for evaluating the performance of wireless communication systems [12, 22, 51–54]. However, with SWIPT, the EE of WPT becomes just as important as the EE of information transmission. Thus, in the following, we focus on three important system design objectives for SWIPT networks, namely, information rate (IR)-EE maximization, energy transfer (ET)-EE maximization, and total transmit power minimization.

5.4.3

System Model In this section, we present a system model for studying MOOP in SWIPT. We assume that the transmitter chooses the transmit signal vector x as 10 Mar 2017 at 08:07:47, .006

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x=

+ wE . ws !"# !"# desired information signal energy signal

(5.25)

Here, wE is a deterministic pseudo-random sequence that is used to facilitate efficient energy transfer and is known to the receivers. Since the energy signal is known at the legitimate receiver, it can be cancelled at the IR via successive interference cancellation before attempting to decode the desired information. As a result, the achievable rate (bit/s) in the SWIPT system is given by   wH Hw C = B log2 1 + 2 + σ2 Tr(HWE ) + σant s   (a) wH Hw ≤ B log2 1 + 2 , (5.26) σant + σs2 where B is the system bandwidth, WE is the covariance matrix of the random energy signals, and (a) is due to the fact that interference cancellation can be performed at the IR to remove hH wE before attempting to decode the desired information. On the other hand, the energy harvested at the ERs is given by HP(w, WE ) =

J 

2 H 2 ηj (|gH j w| + |gj wE | )

j=1

  = Tr G(wwH + WE ) ,

(5.27)

 where G = Jj=1 ηj gj gH j is the equivalent channel of the J ERs introduced in Section 5.3.1. We note that the contribution of thermal noise to the total harvested power is negligible compared with the information and energy signals and thus is neglected in (5.27). On the other hand, we incorporate the total power dissipation of the system as an optimization objective function. To this end, we model the power dissipation (in Joules per second) of the system as TP(w, WE ) =

w2 + Tr(WE ) + NT Pant !" # ξ !" # Antenna power consumption Amplifier power consumption + Pc , (5.28) !"# Constant circuit power consumption

where ξ is the power amplifier efficiency,5 and the first term in (5.28) is the power consumption of the power amplifiers. NT Pant accounts for the dynamic circuit power consumption, which is proportional to the number of transmitting antennas NT . Pant includes the power dissipation of the transmit filter, mixer, frequency synthesizer, digital-to-analog converter (DAC), etc. Pc denotes the fixed power consumption due to the baseband signal processing. 5 We assume that Class A power amplifiers with a linear characteristic are implemented in the transceivers.

In practice, the maximum power efficiency of Class A amplifiers is 25%.

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We define the IR-EE and the ET-EE as ηIR

   H Hw/ σ 2 + σ 2 B log 1 + w 2 ant s C  = = TP(w, WE ) w2 + Tr(WE ) /ξ + NT Pant + Pc

(5.29)

and ηEH =

HP(w, WE ) wH Gw + Tr(GWE )  , = TP(w, WE ) w2 + Tr(WE ) /ξ + NT Pant + Pc

(5.30)

respectively. Now, we first propose three problem formulations for single-objective system design for SWIPT networks. In particular, each single-objective problem formulation considers one important aspect of the system design. Then, we consider the three system design objectives jointly under the framework of multi-objective optimization. The multi-objective optimization framework adopted enables the Pareto optimal beamformer design. The first problem formulation aims at maximizing the IR-EE in the SWIPT network. The problem formulation is given by the following.

Problem 8. Information rate energy efficiency maximization: maximize ηIR w,WE ∈HNT

  subject to C1 : wwH n,n + Tr( n WE ) ≤ Pmaxn , ∀n ∈ {1, . . . , NT } C2 : WE  0 .

(5.31)

The second system design objective is the maximization of the energy transfer efficiency in the SWIPT network and can be mathematically formulated as follows.

Problem 9. Energy transfer efficiency maximization: maximize ηEH w,WE ∈HNT

subject to C1 , C2 .

(5.32)

The third system design objective concerns the minimization of the total transmit power. The problem formulation is given as follows. Problem 10. Total transmit power minimization: minimize w2 + Tr(WE )

w,WE ∈HNT

subject to C1 , C2 .

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(5.33)

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For notational simplicity, we denote the objective functions in Problems 8 and 9 as F8 (w, WE ) and F9 (w, WE ), respectively. We note that Problem 10 is a trivial problem with optimal value zero since the transmitter is not required to provide QoS to the receivers. Yet, Problem 10 plays an important role in the following when we study the beamforming design under the MOOP framework. To facilitate the presentation and without loss of generality, Problem 10 is re-written as an equivalent maximization problem and the corresponding objective function is given by F10 (w, WE ) = −(w2 + Tr(WE )). In practice, the above three optimization objectives are all desirable from the system operator perspective; however, there are non-trivial tradeoffs among these objectives. In order to optimize these conflicting system design objectives systematically and simultaneously, we apply the MOOP framework introduced at the beginning of this section. In particular, we handle the three optimization functions by using the weighted Chebyshev method [17]. Hence, our MOOP is formulated as follows.

Problem 11. Multi-objective optimization problem:   ωj (Fp∗ − Fp (w, WE )) minimize max w,WE ∈HNT p=8, 9, 10

subject to C1 , C2 ,

(5.34)

where Fp∗ is the optimal objective value with respect to Problem p. ωp is a preference  weight imposed on objective function p subject to 0 ≤ ωp ≤ 1 and p ωp = 1, which reflects the preference of the decision maker for the pth objective function over the others. In the extreme case, when ωp = 1 and ωt = 0, ∀t = p, Problem 11 is equivalent to single-objective optimization problem p.

5.4.4

Multi-Objective Optimization Solution In this section, we solve the multi-objective problem optimally by the Charnes–Cooper transformation and SDP relaxation. It can be observed that Problems 8–11 are nonconvex with respect to the optimization variables. In order to obtain a tractable solution, we overcome the non-convexity by recasting the problems as convex problems based on the proposed transformation and SDP relaxation. We first reformulate the aforementioned three single-objective optimization problems by defining a set of new optimization variables as follows: W = wwH , θ =

1 , W = θ W, and WE = θ WE . TP(w, WE )

(5.35)

Then, the original problems can be reformulated in terms of the new optimization variables, i.e., W, WE , and θ , as follows. 10 Mar 2017 at 08:07:47, .006

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Problem 12. Transformed problem 8:  maximize F 8 = θB log2

W,WE ∈HNT ,θ

Tr(HW) 1+ 2 + σ 2) θ (σant s

195



subject to C1 : Tr( n (W + WE )) ≤ θ Pmaxn , ∀n ∈ {1, . . . , NT }, C2 : W  0, WE  0, C3 : Rank(W) ≤ 1, Tr(W + WE ) C4 : + θ (NT Pant + Pc ) ≤ 1, ξ C5 : θ ≥ 0.

(5.36)

Problem 13. Transformed problem 9: maximize

W,WE ∈HNT ,θ

F 9 = Tr(G(W + WE ))

subject to C1 –C5 .

(5.37)

Problem 14. Transformed problem 10:   1 − (NT Pant + Pc ) maximize F 10 = −ξ θ W,WE ∈HNT ,θ subject to C1 –C5 .

(5.38)

Constraints W  0, W ∈ HNT , and Rank(W) = 1 are imposed to guarantee that W = θwwH . Constraints C4 and C5 are introduced due to the proposed transformation. Then, we further transform the MOOP into its equivalent epigraph representation [47] as follows.

Problem 15. Transformed multi-objective optimization problem: minimize

W,WE ∈HNT ,θ,τ

τ

subject to C1 –C5 , C6 : ωp (Fp∗ − Fp ) ≤ τ , ∀p ∈ {8, 9, 10},

where τ is the auxiliary optimization variable. 10 Mar 2017 at 08:07:47, .006

(5.39)

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proposition 5.2. The transformed Problems 12–15 are equivalent transformations of the original Problems 8–11, respectively. In particular, we can recover the solution of the original problems based on (5.35). Proof. Please refer to Section 5.8.2. We note that, if Problem 15 can be solved optimally by an algorithm, then the algorithm can also be used to solve Problems 10–12, since Problem 15 is a generalization of Problems 10–12. Thus, we focus on solving Problem 15 in the following. It can be verified that Problem 15 is non-convex due to the rank-one beamforming matrix constraint in C3 . Now, we apply SDP relaxation by removing constraint C3 : Rank(W) = 1 from Problem 15 in the following. As a result, the SDP relaxed version of Problem 15 is given by the following.

Problem 16. Transformed MOOP – SDP relaxation: minimize

W,WE ∈HNT ,θ,τ

τ

subject to C1 , C2 , C4 –C6 , (( ((( = 1, C :( Rank(W)

(5.40)

3

which is a convex SDP problem and can be solved by numerical convex program solvers such as CVX [48]. Next, we study the tightness of the adopted SDP relaxation in the following theorem. ∗

theorem 5.2. The optimal solution of Problem 16 satisfies Rank(W ) ≤ 1. Besides, this solution can be obtained by construction with a similar approach to that in [49]. Proof. The proof of Theorem 5.2 closely follows the proof of [49, Proposition 1] and is omitted here for brevity. Thus, the adopted SDP relaxation is tight. Besides, similarly to Problem 16, Problems 12–14 can be solved using the SDP relaxation.

5.4.5

Numerical examples In this section, we provide some numerical examples to examine the tradeoff between the conflicting design objectives considered via the proposed optimal beamforming schemes. The system parameters in Table 5.2 are adopted. There are two ERs and one IR located 10 m away from the transmitter. The transmitter is equipped with NT = 12 antennas. The maximum transmit power per antenna is set to Pmaxn = 30 dBm, ∀n ∈ {1, . . . , NT }, the baseband signal processing power consumption is Pc = 1 W, the per-antenna circuit power consumption is Pant = 150 mW, and the power amplifier efficiency is ξ = 0.2. The tradeoff region in Figure 5.10 is obtained by solving Problem 10 Mar 2017 at 08:07:47, .006

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Figure 5.10 Three-dimensional system objective tradeoff regions achieved by the proposed optimal beamforming scheme.

Figure 5.11 Tradeoff region between IR-EE and ET-EE.

15, where the values of 0 ≤ wp ≤ 1, ∀p ∈ {8, 9, 10}, are uniformly varied for a step size  of 0.05 such that p wp = 1. The average system performance is obtained by averaging the obtained results over different channel realizations. Besides, for a better illustration, we have also provided different side-views of the three-dimensional tradeoff region in Figures 5.11–5.13 to reveal the tradeoffs between different pairs of objective functions, namely (1) IR-EE and ET-EE; (2) IR-EE and total transmit power; and (3) total transmit power and ET-EE.

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Figure 5.12 Tradeoff region between IR-EE and the total transmit power.

Figure 5.13 Tradeoff region between total transmit power and ET-EE.

It can be observed from Figures 5.10 and 5.11 that the system design objectives of average ET-EE maximization and average IR-EE maximization are partially aligned with each other for small transmit powers. In particular, both objective functions increase rapidly when the transmit power increases from zero. However, the IR-EE decreases dramatically in the high-transmit-power regime. This is because there is

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a diminishing return in the system achievable rate with respect to the increment in transmit power. Also, we observe similar increasing and then decreasing trends of IR-EE from Figures 5.10 and 5.12 for the tradeoff between IR-EE and the total transmit power, due to the diminishing return in data rate gain achieved by the increment in transmit power. In contrast, ET-EE increases monotonically with respect to the transmit power with increasing slope, see Figures 5.10 and 5.13. Thus, a high transmit power is preferable to maximize the energy transfer efficiency. Furthermore, the tradeoff region in Figure 5.12 is non-convex. In other words, the proposed optimal beamforming scheme is able to attain the non-convex tradeoff region, despite the non-convexity of the MOOP. In fact, the two extremes points in Figure 5.12 correspond to the maximum/minimum of two of the objective functions considered. Zero transmit power represents the minimum total transmit power. It is the optimal value of Problem 10, and it can be obtained by solving Problem 11 with w10 = 1. The second extreme point occurs in the middle of Figure 5.12, which is the maximum IR-EE, i.e., the optimal value for Problem 9. Similarly, the maximum ET can be obtained by solving Problem 11 with w9 = 1. On the other hand, it can be seen from Figures 5.10, 5.12, and 5.13 that the objective of total transmit power minimization conflicts with the other two objectives. In particular, in order to maximize ET-EE, the transmitter has to transmit with almost full power over each antenna at every time instant. The associated beamformers correspond to the single point at the right tail in the curve of Figure 5.10 and the rightmost corner point in Figures 5.12 and 5.13. However, if the transmitter employs a large transmit power, a low IR-EE will result, see Figure 5.12.

5.5

Secure Communications in SWIPT Systems Security is a fundamental problem in wireless communication systems due to the broadcast nature of the wireless medium. Traditionally, cryptographic encryption technologies have been used to enable communication security in the application layer. However, the commonly used encryption algorithms are based on the assumption of limited computational capabilities of the eavesdroppers, which may not hold in the future due to the development of quantum computers. Besides, these algorithms assume a perfect secret key management and distribution, which may not be possible in certain wireless networks such as ad-hoc networks. As an alternative, physical (PHY) layer security utilizes the physical properties of wireless communication channels, such as channel fading and interference, to ensure perfectly secure communication [55–60], regardless of the potentially unlimited computational capabilities of the potential eavesdroppers. On the other hand, in SWIPT systems, transmitters can increase the energy of the information-carrying signal to facilitate energy harvesting at the receivers, see Sections 5.3 and 5.4. However, this may also increase their susceptibility to

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l

na sig on i t a

orm Inf Energy signal Ar tifi cia ln ois e

Transmitter

Information receiver

Energy harvesting receiver 2 (potential eavesdropper)

Energy harvesting receiver 1 (potential eavesdropper)

Figure 5.14 A multiuser SWIPT downlink model with an active IR and J = 2 ERs. The idle receivers harvest energy from the received RF signal and are treated as potential eavesdroppers by the transmitter in terms of providing secure SWIPT services.

eavesdropping6 due to the broadcast nature of wireless channels. Therefore, new QoS concerns regarding communication and energy security naturally arise in systems providing SWIPT services [13, 16, 18, 32, 61, 62]. Thus, in this section, we study beamformer optimization taking into account communication security.

5.5.1

System Model In this section, we present a system model for separated receivers that has commonly been adopted in the literature for secure SWIPT [13, 16, 18, 32, 61, 62], see Figure 5.14. In order to provide secure communication and to facilitate energy harvesting, artificial noise signals and energy signals are generated at the transmitter. In particular, both signals are transmitted concurrently with the information-bearing signal. Besides, they are able to degrade the channels between the transmitter and potential eavesdroppers and act as an energy source for energy harvesting. The transmitter chooses the transmit signal vector x as x=

, + wE + v ws !"# !"# !"# desired information signal energy signal artificial noise

(5.41)

where v ∈ CNT ×1 is the artificial noise vector generated by the transmitter to combat potential eavesdroppers. v is modeled as a complex Gaussian random vector with v ∼ CN (0, V),

(5.42)

6 We note that, in practice, the malicious ERs do not have to decode the eavesdropped information in real time.

They can act as information collectors to sample the received signals and store them for future decoding by other energy-unlimited and powerful computational devices.

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where V ∈ HNT , V  0, denotes the covariance matrix of the artificial noise. The artificial noise signal interferes with the legitimate receiver and potential eavesdroppers since v is unknown to both types of receivers. Hence, artificial noise transmission has to be carefully designed to degrade the channels of potential eavesdroppers while having a minimal effect on the desired receiver. On the other hand, wE is a Gaussian pseudo-random sequence7 that is used to facilitate efficient energy transfer and is known to the legitimate receiver. wE is modeled as a complex Gaussian pseudo-random vector with wE ∼ CN (0, WE ),

(5.43)

where WE ∈ HNT , WE  0, denotes the covariance matrix of the pseudo-random energy signal. Since the energy signal is known at the legitimate receiver it can be cancelled at the legitimate receiver via successive interference cancellation. Besides, the energy signal is not known to potential eavesdroppers and can be exploited by the transmitter to provide communication security. The above system model advocates the dual use of both artificial noise and energy signals in providing secure communication and facilitating efficient WPT. In fact, whether artificial noise or an energy signal is preferable depends on the scenario considered. In order to exploit the energy signal efficiently, a short secret key is needed at the desired receiver as seed information for the pseudo-random sequence generator used for generating the energy signal sequences. Besides, the transmitter is required to regularly change the seed to prevent the sequence from being cracked by potential eavesdroppers. The seed information used at the transmitter can be delivered securely to the desired receivers by exploiting, e.g., the reciprocity of the channels between the transmitter and the legitimate receiver [63]. However, if the seed information is for some reason also available to the potential eavesdroppers, allocating all the energy of the energy signal to the artificial noise may be a better choice for guaranteeing communication security, i.e., WE = 0.

5.5.2

SWIPT for Multiple-Antenna Potential Eavesdroppers In practice, the ERs may be equipped with multiple receive antennas to improve the energy harvesting efficiency. Thus, in this section, we assume that each ER is equipped with NR receive antennas. The received signal at ER j ∈ {1, . . . , J} is given by yERj = GH j x + nERj , ∀j ∈ {1, . . . , J},

(5.44)

where the channel matrix between the transmitter and ER j is denoted by Gj ∈ CNT ×NR . The channel matrices capture the joint effects of multi-path fading and path loss. 2 )I ) is the AWGN at ER j. nERj ∼ CN (0, (σs2 + σant NR

7 For energy transfer, the energy sequence is not required to be generated by a Gaussian pseudo-

random source. However, a Gaussian pseudo-random energy sequence can be exploited to provide secure communication.

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Then, the total amount of power harvested by ER j is given by     H EERj = ηj Tr GH j ww + V + WE Gj .

5.5.2.1

(5.45)

Achievable Rate and Secrecy Rate In this section, we assume that NT ≥ NR to study the beamformer design for providing secure communication. Given perfect CSI at the receiver, the achievable rate (bit/s/Hz) between the transmitter and the IR is given by   wH Hw R = log2 1 + 2 + σ2 Tr(HV) + Tr(HWE ) + σant s   (a) wH Hw ≤ log2 1 + , (5.46) 2 + σ2 Tr(HV) + σant s where (a) is due to the fact that interference cancellation can be performed at the IR to remove hH wE before attempting to decode the desired information. On the other hand, we focus on the worst-case scenario for the decoding capability of the ERs for providing communication security to the IR. We assume that energy harvesting receiver j performs interference cancellation to remove all multiuser interference and eavesdrops on the message intended for the IR. Therefore, the achievable rate between the transmitter and ER j for decoding the signal of the IR can be expressed as H H RERj = log2 det(INR + Q−1 j Gj ww Gj ),

(5.47)

where   2 2 Qj = GH j WE + V Gj + (σant + σs )INR 0 .

(5.48)

Where Qj is the interference-plus-noise covariance matrix for ER j assuming the worst case for communication secrecy. Thus, the achievable secrecy rate of the IR is given by $ %+ Rsec = R − max {RERj } . (5.49) ∀j

5.5.2.2

Problem Formulation In Problem 1, we studied the beamforming design for the maximization of the total power transfer to the ERs. However, this problem formulation does not take into account the fairness in the amount of power harvested per ER. For instance, if there is an ER located closer to the transmitter than other receivers, then the transmitter has a tendency to steer the beamforming direction towards that ER for maximization of the total harvested energy. However, this leads to energy starvation of the other receivers. In order to take into account the fairness in WPT, we formulate the following optimization problem. 10 Mar 2017 at 08:07:47, .006

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Problem 17.

Max–min fairness for secure SWIPT:      H min ηj Tr GH maximize j ww + WE + V Gj

V,WE ∈HNT ,w j∈{1,...,J}

subject to C1 :

wH Hw ≥ req , 2 + σ2 Tr(HV) + σant s

C2 : RERj ≤ RTol ER , ∀j,

$ % C3 : Tr( n V) + Tr( n WE ) + wwH

n,n

≤ Pmaxn ,

∀n ∈ {1, . . . , NT }, C4 : WE , V  0,

(5.50)

where the maximum tolerable data rate RTol ER > 0 in C2 is imposed to restrict the achievable rate of ER j if it attempts to decode the message of the IR. Constraint C4 and WE , V ∈ HNT ensure that the covariance matrices V and WE are positive semidefinite Hermitian matrices. remark 2. We note that the proposed optimization framework can be extended to include additional passive eavesdroppers, for which instantaneous CSI is not available at the transmitter, by introducing probabilistic maximum tolerable SINR constraints for the passive eavesdroppers following a similar approach to that in [16]. Problem 17 is a non-convex optimization problem. In particular, the non-convexity arises from constraint C1 and the log det function in C2 . To overcome the non-convexity, we first advance the following proposition and then recast the problem into a convex optimization problem using SDP relaxation. proposition 5.3. For RTol ER > 0, ∀j, the following implication holds for constraint C2 : C2 ⇒ C2 : GH j WGj  αER Qj , ∀j,

(5.51)

Tol

where αER = 2RER − 1 is an auxiliary constant and C2 is an LMI constraint. We note that constraints C2 and C2 are equivalent, i.e., C2 ⇔ C2 , if Rank(W) ≤ 1. Proof. Please refer to Section 5.8.3 for the proof. Now, we apply Proposition 5.3 to Problem 17 by replacing constraint C2 with constraint C2 . By setting Wk ∈ HNT , ∀k, Wk = wk wH k , and Rank(Wk ) ≤ 1, ∀k, we can rewrite the optimization problem in its hypograph form. 10 Mar 2017 at 08:07:47, .006

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Problem 18. Equivalent formulation of problem 17: maximize

W,V,WE ∈HNT ,τ

τ

  2 + σs2 , subject to C1 : Tr(HW) ≥ req Tr(HV) + σant C2 : GH j WGj  αER Qj , ∀j, C3 : Tr( n V) + Tr( n WE ) + Tr( n W) ≤ Pmaxn , C4 : WE  0, V  0,     C5 : τ ≤ ηj Tr GH j W + V + WE Gj , ∀j, C6 : Rank(W) ≤ 1.

(5.52)

After the transformation, the problem is non-convex due to the rank constraint in C6 . As in the cases studied in the previous sections, we adopt SDP relaxation to obtain a tractable solution. The SDP relaxation of Problem 18 is given by the following. Problem 19.

SDP relaxation of problem 18: maximize

W,V,WE ∈HNT ,τ

τ

subject to C1 , C2 , C3 –C5 , (( Rank(W) C6 : ( ((( ≤ 1 .

(5.53)

It can be verified that the objective function of Problem 18 is an affine function and the constraints span a convex set. Beside, the problem satisfies Slater’s constraint qualification. Thus, the SDP relaxed problem can be solved efficiently in polynomial time via standard numerical solvers for solving convex programs. In the following, we introduce a theorem that reveals the tightness of the adopted SDP relaxation. theorem 5.3. There exists an optimal solution of Problem 18 that satisfies Rank(W) = 1. Besides, this solution can be obtained by construction via a similar approach to that in [18]. Furthermore, V = 0 and constraint C1 is active at the optimal solution. Proof. The proof of Theorem 5.3 closely follows the proof of [18, Proposition 4.1] and is omitted here for brevity.

5.5.3

Numerical Examples In this section, we study the system performance of the proposed beamformer design. The simulation parameters adopted are listed in Table 5.2. We assume that there are 10 Mar 2017 at 08:07:47, .006

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always two ERs and one IR in the system. They are all located 10 m away from the transmitter. The minimum required SNR of the desired IR and the maximum tolerable SINR of the ERs are set to req = 3 dB and −10 dB, respectively. In other words, the maximum tolerable data rate at each ER is RTol ER = 0.1375 bit/s/Hz and the minimum achievable secrecy rate is log2 (1 + req ) − 0.1 = 1.4475 bit/s/Hz.

Average Minimum Harvested Power Figure 5.15 shows the average minimum harvested power per ER versus the maximum transmit power per antenna (dBm) for different numbers of transmit antennas, NT , and different numbers of receive antennas, NR , installed at each ER. It is expected that the average minimum harvested power per ER increases with the maximum transmit power per antenna since the transmitter is able to transfer more power to the RF at every time instant. On the other hand, the minimum harvested power per ER increases both with the number of transmit antennas, NT , and with the number of receive antennas, NR . By increasing the number of transmit antennas, the direction of the energy signal beamforming matrix WE can be more accurately steered toward the ERs, which improves the energy transfer efficiency. Besides, the extra receive antennas at each ER act as extra independent energy collectors to harvest energy from the RF.

800

NT = 8, NR = 1 NT = 8, NR = 2

700 Average minimum harvested power per ER (mW)

NT = 8, NR = 3 NT = 10, NR = 1

600

NT = 10, NR = 2 NT = 10

NT = 10, NR = 3

500

400

NT = 8

300

200

100

0

13

14

15 16 17 18 Maximum transmit power per antenna (dBm)

19

20

Figure 5.15 Average transmit power allocation (dBm) versus the maximum transmit power per antenna, Pmaxn for different numbers of transmit antennas, NT , and receive antennas, NR , installed at each ER.

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Average power allocation (dBm)

206

Number of transmit antennas NT = 8 30 Tr(WE)

Tr(W) 20

10

0

13

14

15 16 17 18 Maximum transmit power per antenna (dBm)

19

20

19

20

Number of transmit antennas NT = 10 30

Tr(WE)

Tr(W)

20

10

0

13

14

15 16 17 18 Maximum transmit power per antenna (dBm)

Figure 5.16 Average transmit power allocation (dBm) versus the maximum transmit power per antenna, Pmaxn , for different numbers of transmit antennas, NT , and receive antennas, NR , installed at each ER.

Average Power Allocation Figure 5.16 depicts the average transmit power allocation to the two components8 of the transmitted signal, i.e., Tr(W) and Tr(WE ), versus the maximum transmit power per antenna for the proposed optimal beamforming scheme. It can be observed that the amount of power allocated to the energy signal is higher than that allocated to the information signal when the required SNR of the IR is low. Besides, the power allocated to the information signal and the energy signal increases as the maximum transmit power per antenna increases because of the higher transmit power budget. In particular, the portion of the total transmit power allocated to the energy signal increases with increasing NT . In fact, the number of degrees of freedom for beamforming increases with the number of transmit antennas. Specifically, with more transmit antennas, the transmitter is able to apply more power-efficient beamforming to the information signal. Thus, a small transmit power is sufficient to satisfy the SINR requirement of the IR in constraint C1 , and more power can be reserved for the energy signal for a more effective transfer of energy to the ERs. 8 As expected from Theorem 5.3, V = 0 holds for the optimal solution. Thus, the power allocated to the

energy signal is not shown in Figure 5.16.

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1.51 NT = 8, NR = 1 NT = 8, NR = 2 Average achivable secrecy rate (bit/s/Hz)

1.5

NT = 10

NT = 8, NR = 3 NT = 10, NR = 1 NT = 10, NR = 2

1.49

NT = 10, NR = 3 Minimum required secrecy rate

1.48

1.47 NT = 8 1.46

1.45

13

14

15

16

17

18

18

20

Maximum transmit power per antenna (dBm) Figure 5.17 Average achievable secrecy rate (bit/s/Hz) versus the maximum transmit power per antenna, Pmaxn for different numbers of transmit antennas, NT , and receive antennas, NR , installed at each ER.

Average Achievable Secrecy Rate Figure 5.17 shows the average achievable secrecy rate versus the maximum transmit power per antenna for the proposed optimal beamforming scheme. It can be observed that the average achievable secrecy rate increases with Pmaxn . This is due to the fact that for larger transmit power budgets the transmitter can allocate more transmit power to the energy signal to degrade the channel of the potential eavesdroppers. Besides, the average achievable secrecy rate increases with the number of transmit antennas NT . The extra degrees of freedom offered by the transmit antennas help in focusing the power of the energy signal at the potential eavesdroppers, which also facilitates efficient jamming. On the other hand, the proposed optimal scheme is able to meet the minimum required secrecy rate even for NR = 3 receive antennas at the potential eavesdroppers.

5.6

Research Challenges The introduction of SWIPT into traditional communication systems revolutionizes the design of beamformers, receiver architectures, and network topologies. It is expected that SWIPT will be a key technology for cutting the last wires of energy-limited low-power-consumption devices to enable truly mobile communications. As discussed 10 Mar 2017 at 08:07:47, .006

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in the previous sections, multiple-antenna technology facilitates SWIPT and at the same time imposes many interesting and challenging new research problems. In the following, we discuss some other fundamental research challenges and potential solutions for realizing SWIPT. Modern communication systems operate in microwave frequency bands for information transfer. Over a short distance of 10 m in free space, the attenuation of a wireless signal can be up to 50 dB for a carrier frequency of 915 MHz in the ISM frequency band. Hence, employing SWIPT in microwave frequency bands directly may result in unsatisfactory performance for long-distance transmission. Three possible approaches to overcome this problem and their potential drawbacks are discussed in the following. •

•

•

Massive MIMO. The extra degrees of freedom offered by massive MIMO facilitate the transmission of narrow energy and information signal beams [64]. In particular, the beams can be more accurately steered toward the receivers to improve system performance. As a result, the combination of massive MIMO and SWIPT seems to be a viable approach to improve the energy transfer efficiency [65]. Nevertheless, the implementation of massive MIMO relies heavily on the availability of cheap and power-efficient radio and base-band hardware. Decreasing the hardware cost and increasing the power amplifier efficiency may have significant negative side effects on the communication link, such as signal distortion and interference. In particular, the non-linearity of the power amplifier can cause the appearance of strong harmonics of the energy-carrying signal that interfere with wireless communications. Thus, the potential benefits of implementing massive MIMO with SWIPT when low-cost non-ideal hardware is adopted at the transmitters remain unknown. Joint beamforming and receiver scheduling. Long-distance transmission is an obstacle to the realization of WPT since the WPT efficiency decreases with distance. As a result, receiver scheduling is a key aspect of facilitating SWIPT in practice. For instance, receivers experiencing high channel gains can be scheduled for WPT and the remaining receivers may be scheduled for information transmission. Also, opportunistic beamforming can be applied to focus the transmitted signals at the targeted receivers. Thus, only a small transmit power is needed from the transmitters so as to improve the power efficiency of the system. Nevertheless, the above receiver scheduling scheme may cause energy starvation in some EH receivers that experience poor channel conditions. Distributed antenna system (DAS). In SWIPT-DAS, dedicated power beacons (stations) and traditional information base stations are distributed across the network and connected to a central processing unit via backhaul links for joint transmission. In particular, the spatial diversity provided by the DAS architecture can effectively combat path loss by reducing the distance between transmitters and receivers. The implementation of DAS for SWIPT relies on information exchange via backhaul links among all transmitters for joint beamforming optimization. Yet, the backhaul capacity can be limited due to the deployment costs of the backhaul links, and full cooperation is impossible. If any power beacons are not connected to the other information transmitters, exceedingly large interference with the information receivers may be created by the power 10 Mar 2017 at 08:07:47, .006

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beacons, which jeopardizes the communication links. Furthermore, the optimal placement of the power beacons and the information base stations is non-trivial and requires thorough study.

5.7

Summary WPT is a fundamental technology that enables self-sustainability of low-power energylimited mobile devices. More importantly, WPT provides the possibility for SWIPT, which introduces a paradigm shift in both system and beamforming design. In this chapter, we have presented a survey of beamforming designs for multiple-antenna SWIPT systems. We first discussed the optimal transmit strategy for maximization of the total power transfer. Then, we focused on system optimization for separated receivers and power-splitting receivers. Our discussion has covered different aspects in SWIPT networks such as physical layer security, multi-objective optimization, and robust beamforming. The beamforming designs for the scenarios considered have been formulated as non-convex optimization problems and were solved optimally via SDP relaxation. Our simulation results have unveiled the potential benefits offered by multiple transmit antennas in improving wireless power transfer efficiency, enhancing spectral/energy efficiency of information transmission, and guaranteeing communication security in SWIPT systems. In addition, future research challenges and some potential solutions for the design of future multiple-antenna SWIPT systems have been discussed.

5.8

Appendix

5.8.1

Proof of Theorem 5.1 Since the relaxed version of problem (5.11) is jointly convex with respect to the optimization variables and satisfies Slater’s constraint qualification, the KKT conditions are necessary and sufficient conditions [47] for the optimal solution of the relaxed problem. In the following, we focus on those KKT conditions which are useful for the proof: Y∗  0, ∗

α ∗ , β ∗ , φj∗ , γn∗ , δ ∗ , θ ∗ ≥ 0

∗

Y W = 0,

(5.55)

Y∗ = INT +

NT 

γn  n −

n=1 ∗

J 

φj Gj − (α ∗ + β ∗ )H

j=1 ∗

= A − (α + β )H, and

(5.54)

(5.56)

*

ρ∗ = *

σs2 α ∗ req , √ σs2 α ∗ req + β ∗ Pmin /η 10 Mar 2017 at 08:07:47, .006

(5.57)

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 T J ∗ ∗ ∗ ∗ ∗ ∗ ∗ where A = INT + N j=1 φj Gj and Y , α , β , φj , γn , δ , and θ are the n=1 γn  n − optimal Lagrange multipliers for (5.13). Equation (5.55) is the complementary slackness condition and is satisfied when the columns of W∗ lie in the null space of Y∗ . Therefore, if Rank(Y∗ ) = NT − 1, then the optimal W∗ = 0 must be a rank-one matrix and the optimal w∗ can be obtained by performing eigenvalue decomposition of W∗ . On the other hand, it can be observed from (5.57) that α ∗ > 0 and β ∗ > 0 at the optimal solution for req > 0 and Pmin > 0. In other words, constraints C1 and C2 are satisfied with equality simultaneously at the optimum point. Now, we prove by contradiction that A is a full-rank matrix with rank NT whenever the condition stated in Theorem 5.1 is satisfied. Let us focus on the dual problem in (5.13). For a given set of optimal dual variables, D = {α ∗ , β ∗ , φ ∗ , γ ∗ , δ ∗ , θ ∗ , Y∗ } and the optimal power-splitting ratio, ρ ∗ , the dual problem in (5.13) can be written as   minimize L W, ρ ∗ , α ∗ , β ∗ , φ ∗ , γ ∗ , δ ∗ , θ ∗ , Y∗ . W∈HNT

(5.58)

Supposing that A∗ is not positive definite, i.e., A∗  0, we can choose W = twwH as a solution of (5.58), where t > 0 is a scaling parameter and w is the eigenvector with respect to one of the non-positive eigenvalues of A∗ . Next, we substitute W = twwH into (5.58), which leads to    Tr(tA∗ wwH ) − t Tr wwH Y∗ + (α ∗ + β ∗ )H + . !" #

(5.59)

≤0

Here  denotes a collection of the variables that are independent of W. On the other hand, since channel vectors gj and h are assumed to be statistically independent, it   ∗  H ∗ ∗ follows that, on setting t → ∞, the term −t Tr ww Y + (α + β )H → −∞ and the dual optimal value becomes unbounded from below. However, the optimal value of the primal problem is strictly positive for req > 0. Thus, strong duality does not hold, which leads to a contradiction. Therefore, A∗ is a positive definite matrix with probability one, i.e., Rank(A∗ ) = NT . By exploiting (5.56) and a basic inequality for the rank of matrices, we have Rank(Y∗ ) + Rank((α ∗ + β ∗ )H) ≥ Rank(Y∗ + (α ∗ + β ∗ )H) = Rank(A) = NT ⇒ Rank(Y∗ ) ≥ NT − 1.

(5.60)

Thus, Rank(Y∗ ) is either NT − 1 or NT . Furthermore, W∗ = 0 is required to satisfy the minimum SINR requirement of the power-splitting receiver in C1 for req > 0. Hence, Rank(Y∗ ) = NT − 1 and Rank(W∗ ) = 1 hold with probability one. In other words, the optimal beamformer w∗ can be obtained by performing eigenvalue decomposition of W∗ and selecting the principal eigenvector as the beamformer. 10 Mar 2017 at 08:07:47, .006

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5.8.2

211

Proof of Proposition 5.2 The proof is based on the Charnes–Cooper transformation [66]. By substituting the new optimization variables in (5.35) into Problem 8, we can rewrite Problem 8 as F8 =

maximize

W,WE ∈HNT ,θ

θ B log2 (1 + Tr(HW)/(θ σ 2 )) Tr(W + WE )/ρ + θ (NT Pant + Pc )

subject to C1 , C2 , C3 , C5 : θ > 0.

(5.61)

Now, we show that the above problem is equivalent to Problem 12. First, it can be observed that in problem (5.61) θ = 0 is not an optimal solution. Thus, without loss of generality, the constraint θ > 0 can be replaced by θ ≥ 0. Second, we prove by contradiction that C4 in Problem 12 is satisfied by equality for the optimal solution, i.e., ∗

∗

Tr(W + WE ) + θ ∗ (NT Pant + Pc ) = 1. ρ ∗

(5.62)

∗

We denote the optimal solution of Problem 12 by (W , WE , θ ∗ ). Suppose that C4 is ∗ ∗ satisfied by strict inequality at the optimal solution, i.e., Tr(W + WE )/ρ +θ ∗ (NT Pant + Pc ) < 1. Then, we construct a new feasible solution by applying a positive scaling to   ∗ ∗ W and θ . The new solution is given by (W , WE , θ  ) = (cW , WE , cθ ∗ ), where    c > 1, such that Tr(W + WE )/ρ + θ (NT Pant + Pc ) = 1. It can be verified that   ∗ ∗ (W , WE , θ  ) achieves a larger objective value in Problem 12 than does (W , WE , θ ∗ ). ∗ ∗ ∗ Thus, (W , WE , θ ) cannot be the optimal solution, which leads to a contradiction. Thus, constraint C4 must hold with equality at the optimal solution. The equivalence of (5.61) and Problem 12 is proved, which implies that Problem 12 is equivalent to Problem 8. In particular, the solution of the original problem can be recovered from (5.35). Similarly, the equivalence of Problems 13–15 and Problems 9–11 can be proved by following the same approach.

5.8.3

Proof of Proposition 5.3 We start the proof by re-writing constraint C2 in the equivalent form

⇐⇒

H Tol C2 : log2 det(INR + Q−1 j Gj WGj ) ≤ RER

(5.63)

−1/2 H −1/2 det(INR + Qj Gj WGj Qj )

(5.64)

≤ 1 + αER .

Then, we propose a lower bound on the left-hand side of (5.64) by introducing the following lemma. lemma 2. For any positive semidefinite square matrix A  0, the following inequality holds [67]: det(I + A) ≥ 1 + Tr(A), where the equality holds if and only if Rank(A) ≤ 1. 10 Mar 2017 at 08:07:47, .006

(5.65)

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Exploiting Lemma 2, the left-hand side of (5.64) is bounded from below by −1/2

det(INR + Qj

−1/2

GH j WGj Qj

−1/2

) ≥ 1 + Tr(Qj

−1/2

GH j WGj Qj

).

(5.66)

Subsequently, by combining equations (5.63), (5.64), and (5.66), we have the following implications: −1/2

(5.63) ⇐⇒ (5.64) ⇒ Tr(Qj

−1/2

⇒ λmax (Qj −1/2

⇐⇒ Qj ⇐⇒

−1/2

GH j WGj Qj

−1/2

GH j WGj Qj −1/2

GH j WGj Qj

GH j WGj

) ≤ αER

 αER Qj .

) ≤ αER

 αER INR

(5.67a) (5.67b) (5.67c) (5.67d)

We note that equations (5.63) and (5.67d) are equivalent, i.e., C2 ⇔ C2 , when Rank(W) = 1.

Acknowledgements This work was supported in part by the AvH Professorship Program of the Alexander von Humboldt Foundation and by the Qatar National Research Fund (QNRF) under project NPRP 5-401-2-161.

References [1] Huawei, Green Energy Solution by Huawei (available at www.huawei.com/en/solutions/gogreener/hw-001339-greencommunication-energyefficiency-emissionreduct.htm). [2] L. Varshney, “Transporting information and energy simultaneously,” in Proc. IEEE International Symposium on Information Theory, July 2008, pp. 1612–1616. [3] P. Grover and A. Sahai, “Shannon meets Tesla: Wireless information and power transfer,” in Proc. IEEE International Symposium on Information Theory, June 2010, pp. 2363–2367. [4] I. Krikidis, S. Timotheou, S. Nikolaou et al., “Simultaneous wireless information and power transfer in modern communication systems,” IEEE Communications Magazine, vol. 52, no. 11, pp. 104–110, November 2014. [5] Z. Ding, C. Zhong, D. W. K. Ng et al., “Application of smart antenna technologies in simultaneous wireless information and power transfer,” IEEE Communications Magazine, vol. 53, no. 4, pp. 86–93, April 2015. [6] X. Chen, Z. Zhang, H.-H. Chen, and H. Zhang, “Enhancing wireless information and power transfer by exploiting multi-antenna techniques,” IEEE Communications Magazine, no. 4, pp. 133–141, April 2015. [7] Powercast Coporation, RF Energy Harvesting and Wireless Power for Low-Power Applications, 2011 (available at www.mouser.com/pdfdocs/Powercast-Overview-2011-01-25.pdf). [8] A. Sample and J. Smith, “Experimental results with two wireless power transfer systems,” in Proc. IEEE Radio and Wireless Symposium, January 2009, pp. 16–18. [9] R. Zhang and C. K. Ho, “MIMO broadcasting for simultaneous wireless information and power transfer,” in Proc. IEEE Global Telecommunications Conference, December 2011, pp. 1–5. 10 Mar 2017 at 08:07:47, .006

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6

Backscattering Wireless-Powered Communications Dinh Thai Hoang

6.1

Introduction The concept of modulating backscatter for communication was first introduced by Stockman in 1948 [1] and promptly received a lot of attention from researchers and developers owing to its potential advantages. Basically, backscatter communication is a technique that allows wireless nodes to communicate without requiring any active radiofrequency (RF) components on the tag [2]. In a conventional backscatter communication system (CBCS), there are two main components, called the wireless tag reader device (WTRD) and the wireless tag device (WTD), as illustrated in Figure 6.1. The WTD in the CBCS is able not only to harvest energy from the received signals, but also to modulate and reflect the signals back to the WTRD. The signal reflection is caused by the intentional mismatch between the antenna and the load impedance at the WTD. Theoretically, when the load impedance is varied, it will generate the complex scatter coefficient which can be used to modulate the reflected signal with information bits. The WTRD then uses the receive antenna to receive reflected signals from the WTD and demodulate these signals to obtain the useful information. In conventional backscattering communication systems, there are two special features that differ from traditional communication systems. First, in conventional backscattering communication systems, the receivers (i.e., WTRDs) have to be equipped with a power source to transmit RF signals to the transmitter (i.e., WTDs). Second, the transmitters do not need to be equipped with a power source to transmit data because they will reflect signals received by the receivers instead of generating their own signals. The second feature is the most important characteristic and also the main objective for the development of conventional backscattering communication systems. This special communication feature of CBCSs has received a great deal of attention, mainly because of the successful implementation of RFID systems and the potential use in sensor devices that are small in size and have a low power supply. Typically, backscattering communication systems operate using RF signals and require the WTRD to be able to transmit RF signals to the WTD. However, a new solution, called ambient backscatter communication, which utilizes RF signals from ambient sources, e.g., TV signals [3] and Wi-Fi signals [4], to help the WTRD to obtain Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

217 10 Mar 2017 at 08:08:07, .007

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Figure 6.1 Conventional backscattering communication system.

Figure 6.2 Ambient backscattering communication system.

data from the WTD without generating RF signals has recently been introduced. To understand how ambient backscatter communication works, let us take Figure 6.2 as an example. In Figure 6.2, there are two battery-free devices, namely node A and node B, which want to communicate with each other, and they are placed near a base station (BS), e.g., a TV tower. We also assume that the BS always transmits RF signals to the surrounding environment, and both node A and node B can receive these signals. Then, when node A wants to send an information packet to node B, node A will backscatter the received RF signals from the BS to convey the bits in the packet. To do so, node A can switch its antenna between reflect and non-reflect mode, corresponding to bit “1” and bit “0,” respectively. After that, when node B receives the signals reflected from node A, it will be able to decode such signals to obtain useful information from node A. It was demonstrated in [3] that one can achieve on information rate between two wireless nodes of up to 1 kbps over distances of 2.5 feet. Recently, with the rapid development of wireless energy harvesting techniques, there have been some new research directions in which such techniques have been adopted in backscattering communication systems. In backscattering communication systems, wireless nodes can reflect received signals to transmit data instead of using their own energy, and thus they do not need to be equipped with energy storage devices. However, in addition to the data transmission process, wireless nodes may need to harvest energy 10 Mar 2017 at 08:08:07, .007

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219

Figure 6.3 Block diagram of backscatter node with RF energy harvesting capability.

for other operations. Therefore, there have been some research works introducing the idea of integrating the energy harvesting circuits into backscatter nodes. The authors of [5] introduced the use of an RF energy harvesting circuit for the backscatter node with the aim of supplying power for the controller. As shown in Figure 6.3, the harvested energy from RF signals will be used to supply power for the micro-controller. In addition, which is different from conventional backscatter communication systems, the authors in [5] introduced a switch (MOSFET Avago ATF-54143) in order to adjust the impedance of the antenna with the aim of being able to control the reflected power at the antenna, resulting in a sequence of bits 0 or 1 at the gate. Furthermore, in the proposed system, the authors combined the backscatter system and the wireless power transfer (WPT) system at two different frequencies. They aimed at modulating the signals received from its reader at one frequency and harvesting energy at the other frequency concurrently. As a result, both the WPT and the backscatter system can be beneficial in terms of the harvested power and RF–DC conversion efficiency. The authors of [6] extended the scenario studied in [5] to multi-antenna wireless energy transfer. As illustrated in Figure 6.4, the tag reader is equipped with a bistatic antenna configuration, i.e., it can use M antennas to transmit data and R antennas to receive data simultaneously. The authors then proposed optimal solutions for resource allocation for both single- and multi-tag cases. Numerical results showed that the proposed system is a promising and efficient framework for low-power and low-cost wireless systems. Differently from [5] and [6] which considered integrating RF energy harvesting circuits for backscattering communications, the authors of [7] studied a new kind of WPT to improve the data transmission for backscatter communication systems. In particular, the authors of [7] adopted ultra-wideband and multisine signals [8] to increase the efficiency of WPT, thereby improving the reading range of RFID readers. The experiments then demonstrated that a maximum reading range of the reader of 7.8 m could be achieved. All of the above works concern backscatter communication systems in which RF signals are adopted as a means to convey information for wireless nodes. Such backscatter communication systems are known as far-field backscatter communication systems (FF-BCSs). Recently, with the rapid development of near-field WPT techniques, there has been some new research studying the use of such techniques in backscatter 10 Mar 2017 at 08:08:07, .007

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Figure 6.4 Ambient backscattering communication system.

Figure 6.5 Near-field backscattering communication system.

communication systems, and these systems are known as near-field backscatter communication systems (NF-BCSs). Differently from FF-BCSs which use RF signals as a means to transfer data, NF-BCSs adopt magnetic field as a means to supply power to the WTDs and also to transfer data from WTDs to WTRDs. As a result, instead of using antennas for communications, in NF-BCSs, WTDs and WTRDs use coupled coils for communications, as shown in Figure 6.5. 10 Mar 2017 at 08:08:07, .007

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In NF-BCSs, there are two main phases, namely power supply and data transfer. In the first phase, i.e., power supply, the WTRD transfers energy to the WTD by using the inductive coupling technique. In particular, when there is an electric current moving through a wire coil (L1), it will generate a magnetic field and, if a second wire coil (L2) is placed in this magnetic field, a current can be induced in the second wire coil by the magnetic field as illustrated in Figure 6.5. Then, in the second phase, i.e., data transfer, as in FF-BCSs, the WTD can turn on/off at the load resistor, thereby changing the impedance ZT . Consequently, the change in the impedance ZT yields voltage changes at the WTRD. Specifically, when the impedance of the WTD is varied, it will influence the amplitude modulation of the voltage UL at the WTRD’s coil. Therefore, if the on/off switching of the load resistor is controlled by the data flow, these data can be transferred to the WTRD by detecting the change of the voltage at the WTRD’s coil [9]. This kind of data transfer is known as load modulation. In the United States, FF-BCSs typically operate in the unlicensed frequency bands available at 902–928 MHz and 2400–2483.5 MHz, but most FF-BCS applications are in the range 902–928 MHz. Alternatively, there is a band range, i.e., the 5725–5850 MHz ISM band, which is also used for FF-BCSs due to its potential benefits as stated Table 6.1. Summary of applications of wireless energy harvesting in backscattering communication systems Reference

EH

BT

Purpose

Results

[3] (2013)

Far-field

Ambient backscatter

[4] (2014)

Far-field

Ambient backscatter

Information rates of up to 1 kbps over distances of 2.5 feet and 1.5 feet can be achieved Communication rates of up to 1 kbps over a the distance of 2.1 m can be achieved

[5] (2015)

Far-field

Conventional backscatter

[6] (2015)

Far-field

Conventional backscatter

[7] (2015)

Far-field

Conventional backscatter

Leverage existing TV and cellular transmissions to eliminate the need for wires and batteries Demonstrate the possibility of reusing existing Wi-Fi infrastructure to provide Internet connectivity to RF-power devices Prove that using two different tones with the same power results in a continuously energy beam system Optimize the resource allocation to maximize the total utility of harvested energy for multi-antenna backscatter communication systems Improve the data transmission range for backscatter communication systems

10 Mar 2017 at 08:08:07, .007

The proposed system can be beneficial in terms of the harvested power and RF–DC conversion efficiency Under the proposed optimization solution, the harvested energy suffers a slight reduction of less than 10% A maximum reading range of the reader of 7.8 m can be achieved

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in [10]. In contrast to FF-BCSs which operate at ultra-high frequency (UHF), NF-BCSs often work in the high-frequency range, i.e., 13.56 MHz, or the low-frequency range, i.e., 125–134 MHz. As a result, applications of NF-BCSs are limited by the distance between the tag and the tag reader. In Table 6.1, we summarize applications of wireless energy harvesting techniques in backscatter communication systems. As shown in Table 6.1, there has been quite a lot of research on this topic, all of it very new (since 2013). Thus, I believe that this topic will receive a lot of attention in the next few years. In addition, most of the current work concern far-field backscatter communications, while near-field backscatter communications, which have advantages such as high data transmission rates, have not been well investigated. Thus, in the next section, we will introduce an application of near-field backscatter communication systems with the aim of increasing the distance between the WTD and the WTRD over which communication is possible.

6.2

Application of Backscattering Communication in Wireless-Powered Body Area Networks

6.2.1

Motivations Recently, from both academia and industry, there has been an increasing interest in wireless body area networks (BANs). BANs, benefiting from advanced technologies such as ultra-low power, microelectronics, and smart monitoring sensors, have been applied to many applications [11], e.g., healthcare, military applications, sport, and entertainment. A BAN is a collection of sensors implanted, attached, or worn on a human body. The sensors collect various data about physiological changes in the human body. Then, the data are transmitted to a data collection point, e.g., a gateway, to extract useful information. Although BANs are very useful, there are still many open issues that have not been addressed, e.g., data communication and energy supply, as highlighted in [11] and [12]. Typical sensors in BANs have to operate on a battery energy supply. However, using a battery poses many problems, e.g., big size, large weight, high cost, limited capacity, complicated maintenance, and difficulty of charging or replacing. Additionally, it can cause harmful effects, e.g., generating heat, to a human body [11–13]. Therefore, energy harvesting such as from vibration and body heat is a suitable solution that is adopted in BANs. Recently, wireless energy harvesting and transfer has been used for sensor networks. They are more flexible and more predictable, e.g., they are powered from a dedicated energy source, than the other energy harvesting techniques. Thus, the wireless energy harvesting and transfer technique is a good candidate for BANs. In this section, we study two major issues in BANs, i.e., data communication and energy transfer. We consider wireless energy harvesting and transfer (WEHT) [13] for sensors in BANs, which is called wireless-powered BAN (WPBAN). Using WEHT, the sensors can work continuously without needing any physical connections for charging or battery replacement, thereby improving convenience and flexibility. WEHT can be based on magnetic resonance coupling, and the electromagnetic backscatter coupling technique used in radio-frequency identification (RFID) [9] can be employed in WBANs. In a WPBAN, data from the sensor can be transmitted when the gateway transfers energy to that sensor. Thus, data transmission and energy harvesting processes 10 Mar 2017 at 08:08:07, .007

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can be performed simultaneously, and there is no need to rely on energy storage for the sensors. This not only reduces complexity in designing the sensors, but also significantly increases the energy and communication efficiency of WPBANs. However, in the WPBAN under consideration, the energy of the gateway is limited, and data transmission of different sensors has to be prioritized according to importance. Moreover, although the implementation of magnetic resonance coupling and the electromagnetic backscatter coupling technique in WPBANs is expected to yield many advantages, it still needs an optimal energy transfer decision for the gateway. In particular, with magnetic resonance coupling and electromagnetic backscatter coupling, data from a sensor are transmitted only when the gateway transfers energy to that sensor. However, in practice, many environment and system parameters can be unknown to the gateway, and thus a centralized control approach that requires complete network information may not be possible. We study the energy transfer and data transmission optimization for WPBANs with magnetic resonance coupling and the electromagnetic backscatter coupling technique. The energy transfer and data transmission scheduling problem concerns different priority of sensors and importance of data. We formulate an optimization problem and develop algorithms to obtain an optimal solution for the gateway. •

•

•

•

6.2.2

We first formulate the optimization problem of the gateway in the WPBAN as a Markov decision process (MDP). The optimization aims to find an optimal energy transfer and data transmission policy that minimizes the cost defined in terms of the average packet delay, which also mitigates the average packet loss of the system. The optimization considers that different sensors have different priority, and for each sensor, different data have different degrees of importance, depending on the applications. We then introduce the state–action–reward–state–action (SARSA) algorithm to obtain the optimal policy. The algorithm overcomes the curse-of-model issue when some parameters are not known in advance and helps the gateway make an optimal decision in an online fashion. We investigate the use of approximation functions and introduce a learning algorithm, called SARSA, with a linear function approximation. This algorithm addresses the curse of dimensionality when the state space of the problem becomes too large. We analytically show the convergence of the algorithm. Through simulations, we show that the proposed learning algorithm can effectively optimize the energy transfer and data transmission policy of the WPBAN. In particular, we investigate the impacts of parameters on the network performance. Moreover, we consider two different feature functions used in the linear approximation functions and compare them in terms of the average cost, the average energy, and the average packet loss. We find that, when we adopt more key features, the performance can be improved, but at the cost of higher complexity.

Sensor Operation, System Model and Scheduling In this section, we first explain the underlying mechanism of using magnetic resonance coupling and the electromagnetic backscatter coupling technique for body 10 Mar 2017 at 08:08:07, .007

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sensors. Then, we introduce the system model for a wireless-powered body area network (WPBAN) and design an optimization framework for the proposed system model.

6.2.2.1

Sensor Operation A sensor can use magnetic resonance coupling [14] for energy supply. It has many advantages. First, magnetic resonance coupling has a high energy transfer efficiency, especially over a short distance, e.g., up to 93% [15]. Second, with magnetic resonance coupling, the energy transfer and data transmission can be performed simultaneously without causing interference to far-field communications, e.g., Wi-Fi and 3G/4G networks. Third, the energy used in the magnetic field can be transferred through the human body with little or no hormfull effect on human health. Fourth, with magnetic resonance coupling, the gateway can transfer energy to multiple nodes simultaneously. Next, we will study how to integrate the mechanisms of magnetic resonance coupling and electromagnetic backscatter coupling to a body sensor in terms of the principle of reflection via antenna coil switching, so that the sensor can transmit data in a way that does not require an energy buffer. To do so, the sensor (the receiver) needs to be equipped with load modulation as illustrated in Figure 6.6, which will be used for conducting communications. The transmitter (i.e., the gateway) is equipped with an impedance resonance matching circuit using the adaptive frequency tuning technique [16] in order to enhance the energy transfer efficiency. In this case, when the transmitter transfers power to the receiver, the receiver will generate a reflected wave by adjusting a load modulation. This wave carrying data is then received and decoded by the gateway as illustrated in Figure 6.6 [17]. Therefore, the receiver does not need to have an energy buffer to store harvested energy since the energy transfer and data transmission are performed concurrently through its own coils.

6.2.2.2

System Model and Scheduling We now explain backscatter magnetic resonance coupling and propose a communication model for wireless body sensors. We assume that each sensor has a data queue as illustrated in Figure 6.7 to store data before transmitting them to the gateway.

The transmitter coil obtains information by detecting the change of its resonance state. Controller

Controller

Information R1

R1

CR3

R +Eoo

Sensor

Data buffer

Modulator circuit Receiver

Load modulation

Receiver coil

Electrical power

CR3

R

Transmitter +Eoo coil Impedance resonant Demodulator matching circuit circuit (Turning circuit)

Energy buffer

Display or/and communicate with other devices

Transmitter The receiver receives electrical power from the transmitter coil and then uses the load modulation to make the change to the transmitter resonant’ state.

Figure 6.6 An illustration of using the magnetic resonance wireless power transfer method with

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Figure 6.7 System model.

The data are classified by the sensor according to the importance of the information. We consider two types of data, namely normal and important data. For example, with smart bandages, skin temperature measurements are normal data, whereas tissue damage detection constitutes important data. After the classification, the data are packetized and stored in the data queue of the sensor if the data queue is not full. If the data queue is full, and a normal packet arrives, the normal packet which has remained longest in the queue will be removed from the queue, and the newly arriving normal packet will be put into the data queue. However, if the data queue is full of important packets, the newly arriving normal packet will be dropped. Similarly, when a new important packet arrives, and the data queue is full, the normal packet which has remained longest in the queue will be removed from the queue, and the newly arriving important packet will be put into the data queue. However, if a new important packet arrives and the queue is full of important packets, the important packet which has remained longest in the queue will be removed from the queue so that the new incoming important packet can be stored in the queue. Additionally, if the sensor is allowed to transmit a packet and the data queue contains both normal and important packets, the sensor will transmit an important packet first. This queuing policy is designed to ensure that the important data have higher priority, and the data will be transmitted to the gateway to inform the user or external party at the earliest time possible. We study the scheduling problem for the WPBAN. The objective is to minimize the cost defined in terms of the average packet delay and the packet loss for sensors. In the WPBAN, multiple sensors collect data from a human body or from the environment, and the data is transmitted to the gateway attached to the user’s body. The gateway has its own battery, and it is charged randomly, e.g., as a consequence of user mobility. Note here that, while the gateway visits the charger, the data collected from the sensors can be uploaded to the server. For the scheduling of energy transfer and data transmission, we assume that the system is slotted, and there are three phases in each time slot as shown in Figure 6.8. In the first phase, the gateway collects information from all sensors in the network by applying multi-access procedures with anti-collision measures [9] (Chapter 7), which 10 Mar 2017 at 08:08:07, .007

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Phase 1: Collect data from sensors Initial time

Phase 2: Gateway decision Phase 3: Gateway performance

t=0

Time A time slot

Figure 6.8 Time-slot structure.

are widely used in practice. Specifically, the gateway first broadcasts power to sensor nodes, and then these sensors use that energy to send back information to the gateway. To avoid collisions among data flows sent to the gateway, the gateway can adopt one of several anti-collision multi-access methods, e.g., time division multiple access (TDMA). The information which is sent from a sensor to the gateway including the status of the data queues, the type of sensor, and the channel quality, e.g., the distance from the sensor to the gateway, is very small in size, so we can assume that the amount of energy used in the first phase by the gateway is trivial. From information collected, in the second phase, the gateway will make a decision to sleep, to allow one of sensors to transmit data, or to receive energy from the charger, if the charger is nearby. In the third phase, the gateway performs the action determined in the second phase and updates the current state of the system. The total number of sensors in the network is N, and the maximum data queue size of sensor n is Dn . The packet arrival probability of node n for normal data is pm n , and that for important data is pin . The distance from sensor n to the gateway at time slot t is cn (t), and to transmit data from sensor n at distance cn (t) the gateway consumes e(t) units of energy from its battery. The maximum battery size of the gateway is denoted by E units of energy, and the probability that the gateway meets the charger is pc . When the gateway is in the charging area of a charger, it can receive eg (t) units of energy. Different sensor nodes have different priorities, and we denote the priority factor of node n by σn . Similarly, we denote the weights of important and normal packets by δ i and δ m , respectively.

6.2.3

Optimization Formulation In this section, we formulate the cost optimization for the scheduling problem of WPBANs as a Markov decision process (MDP). Typically, an MDP is defined by a tuple S, A, T, R, where S is the system state space, A is the system action space, T is the transition probability matrix of the system, and R is the reward or cost function.

6.2.3.1

State Space The state space of the system is defined as follows: S  S † × E × V, 10 Mar 2017 at 08:08:07, .007

(6.1)

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where × is the Cartesian product, S † = S1 × · · · × Sn × · · · × SN is the composite state space of all sensors in the network, E = {0, 1, . . . , E} represents the set of energy levels of the gateway, and V = {0, 1} expresses the energy supply state space of the charger. Sn is the state space of sensor n that is defined by Sn = Dnm × Dni × Cn , where dnm ∈ Dnm = {0, 1, . . . , Dn } is the number of normal packets, dni ∈ Dni = {0, 1, . . . , Dn } is the number of important packets in the data queue of node n, and cn ∈ Cn = {0, 1} is the distance state from the sensor n to the gateway, with 0 and 1 corresponding to the near and far states, respectively. Note that we have dnm + dni ≤ Dn . For cn = 0 or cn = 1, the gateway needs to use en or ef (ef > en ) units of energy to transfer wireless energy and collect data from the sensor, respectively. Finally, v ∈ V is the charger visit state of the gateway. For v = 1 and v = 0, the gateway visits and does not visit the charger, i.e., the gateway can and cannot receive energy from the charger, respectively.

6.2.3.2

Action Space The action space is defined by   A  a : a ∈ {0, 1, 2} ,

(6.2)

where ⎧ ⎨ 0, a= 1, ⎩ 2,

the gateway does nothing (sleep), the gateway allows one of the sensors to transmit data, the gateway harvests energy from the charger.

 Note that 1 = (x1 , . . . , xn , . . . , xN ), where xn ∈ {0, 1} and N n=1 xn = 1. In other words, there is at most one sensor allowed to transmit data in a time slot. Additionally, the action space given the current state s ∈ S of the system, i.e., As , comprises all possible actions that do not make a transition to the state that is not allowed. We can express the action space As as follows: ⎧  (dm + di ) = 0, {0}, if v = 0 and N ⎪ n=1 ⎪ N n m n i / ⎪ ⎪ ⎪ OR if v = 0 and n=1 (dn + dn ) > 0 and N cn = 0 and e < en , ⎪ ⎪  /n=1 ⎪ N N m i ⎪ OR if v = 0 and n=1 (dn + dn ) > 0 and n=1 cn > 0 and e < ef , ⎪ ⎪  ⎪ ⎪ m i n f ⎪ OR if v = 0 and N ⎪ n=1 (dn + dn )(1 − cn ) = 0 and e ≤ e < e , ⎪  ⎪ N m i ⎪ OR if v = 1 and n=1 (dn + dn ) = 0 and e = E, ⎪ ⎪ N ⎪ ⎪ m ⎪ {1}, if di ) > 0 and e = E, ⎪ n=1 (dn + ⎪ Nn m ⎨ {2}, if v = 1 and n=1 (dn + dni ) = 0 and e < E,  /N As = m i n ⎪ OR if v = 1 and N ⎪ n=1 (dn + dn ) > 0 and /n=1 cn = 0 and e < e , ⎪  ⎪ N N m i ⎪ OR if v = 1 and n=1 (dn + dn ) > 0 and n=1 cn > 0 and e < ef , ⎪ ⎪  ⎪ m i n f ⎪ ⎪ OR if v = 1 and N n ) = 0 and e ≤ e < e , ⎪ n=1 (dn + dn )(1 − c ⎪  / ⎪ N N m i n ⎪ {0, 1}, if v = 0 and n=1 (dn + dn ) > 0 and n=1 cn = 0 and e ≤ e < E, ⎪ ⎪  /N ⎪ m i f ⎪ ⎪ OR if v = 0 and N ⎪ n=1 (dn + dn ) > 0 and n=1 cn > 0 and e ≤ e < E, ⎪  / ⎪{1, 2}, if v = 1 and N (dm + di ) > 0 and N c = 0 and en ≤ e < E, ⎪ ⎪ n=1 n=1 ⎪  n mn i /Nn ⎩ f OR if v = 1 and N (d + d ) > 0 and n n=1 n n=1 cn > 0 and e ≤ e < E. (6.3) 10 Mar 2017 at 08:08:07, .007

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Here, we do not have two combinations, i.e., {0, 2} and {0, 1, 2}, because they are the same as the cases of {2} and {1, 2}, respectively. The reason is that, when the gateway visits the charger and the energy buffer is not full, the gateway will prefer to receive energy from the charger or to transfer energy to a sensor to collect data instead of doing nothing.

6.2.3.3

Transition Probability Matrix We express the transition probability matrix of the system T(a) given the action a ∈ A as follows: ⎤ ⎡ ←e=0 G0,0 (a) G0,1 (a) G0,2 (a) · · · G0,E (a) ⎢ G1,0 (a) G1,1 (a) G1,2 (a) · · · G1,E (a) ⎥ ← e = 1 ⎥ ⎢ (6.4) T(a) = ⎢ ⎥ . .. .. .. .. .. ⎦ .. ⎣ . . . . . GE,0 (a) GE,1 (a)

GE,2 (a)

···

GE,E (a)

←e=E

where each row of matrix T(a) corresponds to the energy level of the gateway. In particular, this transition probability matrix captures the energy level change of the gateway when action a is taken. For example, when the energy level is 0, if the gateway visits the charger and the gateway takes action “charging,” the system state transitions to G0,1 . Here, we assume that the gateway can receive one unit of energy from the charger successfully. Then, the transition probability matrix of Ge,e (a) can be expressed as follows: ⎤ ⎡ d0,1 (a) d0,2 (a) · · · d0,|S † | (a) d0,0 (a) ←d=0 ⎥ ←d=1 ⎢ d1,0 (a) d (a) d (a) · · · d † | (a) 1,1 1,2 1,| S ⎥ ⎢ Ge,e (a) = ⎢ ⎥ . .. .. .. .. .. ⎦ .. ⎣ . . . . . ← d = |S † | (6.5) where each row of matrix Ge,e (a) corresponds to the state of a sensor. |S † | is the total size of the state space S † , and d ∈ S † is the state index of the state space S † , which can be determined through the current states of all sensors in the networks, i.e., the number of important packets, the number of normal packets, and the distance states from all sensor nodes to the gateway. The fact that the number of states in the state space S † is very large leads to the difficulty in determining specific transition probabilities for all cases in the system. For example, even with only two sensor nodes and each sensor node having the maximum data queue size of five packets, the number of states is |S † | = (21×2)2 = 1764, rendering the derivation of all possible transition probabilities intractable; this is the curse of dimensionality. Moreover, there are some parameters that it may not be possible to obtain in advance, e.g., the charger visit probability and the packet arrival probabilities; this is the curse of the model. Therefore, in the next section, we will introduce learning algorithms as the solution to these issues. d|S † |,0 (a) d|S † |,1 (a) d|S † |,2 (a)

6.2.3.4

···

d|S † |,|S † | (a)

Reward Function The gateway aims to minimize the weighted queue length corresponding to data of different types, which also indirectly minimizes the average packet loss for the system. 10 Mar 2017 at 08:08:07, .007

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Therefore, we define the immediate cost function as follows: C=

N 

σn (δ m dnm + δ i dni ),

(6.6)

n=1

where σn is the priority factor of node n. δ m and δ i are the weights of normal and important packets, respectively. dnm and dni are the numbers of normal and important packets of node n, respectively. Therefore, the reward function at state st after action at has been taken and the system has transitioned to state st+1 can be defined as follows: R(st , at , st+1 ) = −

N 

  σn δ m dnm (t + 1) + δ i dni (t + 1) .

(6.7)

n=1

Here, the reward to be maximized is the negative cost.

6.2.4 6.2.4.1

The Optimal Policy for the Gateway The Q-Learning Algorithm

In the WPBAN, we aim to find an optimal policy π ∗ : S → A for the gateway to minimize the overall cost for the system. Accordingly, we first define a value function V π : S → R that represents the expected value obtained by following policy π from each state s ∈ S. The value function V for policy π quantifies the goodness of the policy through an infinite horizon and discounted MDP that can be expressed as follows: ) (∞ % $  γ t Rt (st , at )|s0 = s = Eπ rt (st , at ) + γ V π (st+1 )|s0 = s , (6.8) V π (s) = Eπ t=0

where 0 ≤ γ < 1 is a discount factor, and rt (st , at ) represents the immediate reward achieved at state st after action at has been taken. Since we aim to find the optimal policy π ∗ , an optimal action at each state has to be found through the optimal value function expressed as follows:    V ∗ (s) = max Eπ rt (st , at ) + γ V π (st+1 ) . (6.9) a

  If we denote Q∗ (s, a)  rt (st , at ) + γ Eπ V π (st+1 ) as the optimal Q-function for all state–action pairs, then the optimal value function can be written as follows:   (6.10) V ∗ (s) = max Q∗ (s, a) . a

Now, the problem is reduced to determining an optimal value of the Q-function, i.e., Q∗ (s, a), for all state–action pairs, and this can be done through making samples iteratively. In particular, the Q-function is updated according to the following rule: % $ (6.11) Qt+1 (s, a) = Qt (s, a) + αt rt (s, a) + γ max Qt (s, a ) − Qt (s, a) . a

The core idea behind this rule is to find the temporal difference between the predicted Q-value, i.e., rt (s, a)+γ maxa Qt (s, a ), and its current value, i.e., Qt (s, a). In (6.11), the learning rate αt is introduced to determine the impact of new information on the existing 10 Mar 2017 at 08:08:07, .007

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value. The learning rate can be chosen to be a constant, or it can be adjusted dynamically during the learning process. However, it must satisfy the following assumption in order to guarantee convergence for the Q-learning algorithm. assumption 1. The step size αt is deterministic, non-negative and satisfies the following conditions: αt ∈ [0, 1],

∞ 

αt = ∞, and

t=1

∞  (αt )2 < ∞.

(6.12)

t=1

The step size adaptation αt = 1/t is one of the most common examples used in reinforcement learnings. More discussion on selecting an appropriate step size can be found in [18]. The details of the Q-learning algorithm are provided in Algorithm 6.1. Algorithm 6.1 The Q-learning algorithm Input. For each state–action pair (s, a), initialize the table entry Q(s, a) arbitrarily, e.g., to zero. Observe the current state s, initialize a value for the learning rate α and the discount factor γ . for t := 1 to T do From the current state–action pair (s, a), execute action a and obtain the immediate reward r and a new state s . Select an action a based on the state s and then update the table entry for Q(s, a) as follows: % $ Qt+1 (s, a) ← Qt (s, a) + αt rt (s, a) + γ max Qt (s , a ) − Qt (s, a) . (6.13) a

s .

Replace s ← end for Output. π ∗ (s) = arg maxa Q∗ (s, a). Once either all Q-values have converged or a certain number of iterations has been reached, the algorithm will be terminated. This algorithm yields an optimal policy indicating an action to be taken at each state such that Q∗ (s, a) is maximized for all states in the state space, i.e., π ∗ (s) = arg maxa Q∗ (s, a). Under the assumption of the step size (i.e., Assumption 1), it was proved in [19] that “Q-learning converges to the optimum action-values with probability one so long as all actions are repeatedly sampled in all states and the action-values are represented discretely.” remark 1. In practice, action a can be selected using a popular method, i.e., the -greedy strategy. This strategy introduces a parameter , which suggests for an agent choosing a random action with probability , and otherwise the agent will select an action that maximizes Q(s, a). This strategy is necessary for exploring the whole state space. Thus, in a Q-learning algorithm, we need to establish a balance between the exploration time, i.e., , and the exploitation time, i.e., 1 − . 10 Mar 2017 at 08:08:07, .007

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231

SARSA: An Online Q-Learning Algorithm Although through using the Q-learning algorithm we can find an optimal policy for the gateway without requiring knowledge of the environment, the algorithm works in an offline fashion. In particular, Algorithm 6.1 can obtain the optimal policy only after the iterations have been terminated, i.e., when the Q-values converge. Therefore, in this section, we consider an alternative online learning algorithm, i.e., the SARSA algorithm (Algorithm 6.2). Algorithm 6.2 SARSA: An online Q-learning algorithm Input. For each state–action pair (s, a), initialize the table entry Q(s, a) arbitrarily, e.g., to zero. Observe the current state s, initialize a value for the learning rate α and the discount factor γ . for t := 1 to T do From the current state–action pair (s, a), execute action a and obtain the immediate reward r and a new state s . Select an action a from As using a policy derived from the Q-learning policy, e.g., -greedy, and then update the table entry for Q(s, a) as follows: % $ (6.14) Qt+1 (s, a) ← Qt (s, a) + αt rt (s, a) + γ Qt (s , a ) − Qt (s, a) . Replace s ← s and a ← a . end for Differently from the Q-learning algorithm, the SARSA algorithm is an online algorithm that allows the gateway to choose optimal actions at each time epoch in a real-time fashion without waiting until the algorithm has converged. In the Q-learning algorithm, the policy is updated on the basis of the maximum reward of available actions regardless of which policy is applied, i.e., it is an off-policy method. In contrast, the SARSA algorithm interacts with the environment and updates the policy directly from the actions taken, i.e., it is an on-policy method. Note that the SARSA algorithm updates Q-values from the quintuple Q(s, a, r, s , a ), where s and a are the current state and action, r is the immediate reward obtained after action a has been taken, and s and a are the new state–action pair. The parameters α and γ have the same meaning as in Algorithm 6.1. Since the SARSA algorithm is an online learning algorithm its conditions for convergence are highly dependent on the selected learning policy. Therefore, to achieve convergence to optimality for the SARSA algorithm, it was shown in [20] that the selected learning policy must be greedy in the limit of infinite exploration (GLIE). In particular, a policy is GLIE if all states are infinitely visited and each action is executed an infinite number of times. One example of GLIE is -greedy policy as mentioned in Remark 1. Then, the convergence of the SARSA algorithm as given in Algorithm 6.2 is proved in Theorem 6.1. theorem 6.1. The sequence {Qt } converges to Q∗ with probability one, and the sequence {πt } converges to π ∗ if the following conditions are satisfied. 1. 2.

The Q-values are stored in a lookup table. ∞ 2 αt ∈ [0, 1], ∞ t=1 αt = ∞, and t=1 (αt ) < ∞. 10 Mar 2017 at 08:08:07, .007

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3. 4.

Var[rt (s, a)] < ∞. {πt } is greedy in the limit of infinite exploration (GLIE).

In Theorem 6.1, the second condition guarantees that the step size of Algorithm 6.2 approaches zero when the time goes to infinity. The third condition (i.e., the variance function of the immediate reward function is lower than infinity) implies that the immediate reward function is bounded, and the fourth condition enforces learning policies to follow the GLIE. The detailed proof of Theorem 6.1 can be found in [20].

6.2.4.3

SARSA with Linear Function Approximation With the SARSA algorithm, we can apply optimal policies for the gateway in an online fashion such that at each time slot the gateway can select the best action to optimize its objective function without having knowledge about the environment. However, when we implement Algorithm 6.2 for the gateway, it requires the gateway to store a lookup table for all Q-values. For instance, if we have two sensor nodes with the maximum data queue size of five packets, and the maximum energy buffer capacity of the gateway is 10 units of energy, the total number of states is 422 × 22 = 38,808. Then, if we have around four actions per state, then the number of Q-values in the lookup table will be 155,232, which is intractable, especially when the number of sensors grows. Additionally, a large state space requires much longer experiments to collect enough information for a successful learning process. To address the curse-of-dimensionality issue, we adopt a common approach from machine learning for representing values, i.e., the linear function approximation. By adopting an appropriate feature function φ(s, a), which may yield similar feature vectors for similar state–action pairs, we can provide a generalization over the state space and the action space for a specific task. If such a function is satisfied, the Q-value function can be approximated as a linear combination of these features as follows: Qπ (s, a) ≈ Qθπ (s, a) =

F 

φf (s, a)θf = φ  (s, a)θθ ,

(6.15)

f =1

of feature f , and  represents where F is the total number of features, θf is a weighting    the transpose operation. Here, we denote φ (s, a) = φ1 · · · φf · · · φF . Now, instead of learning the optimal Q-values for it is sufficient   all state–action pairs directly, to learn the vector of weightings θ  = θ1 · · · θf · · · θF , which can lead to an approximation of the Q-function. Given the approximation function, we aim at minimizing the mean-square error (MSE) over a probability distribution Z of the state space S, i.e., $ % (6.16) ζ (θθ ) = EZ (Qπ (s, a) − Qθ (s, a))2 , where Qπ (s, a) is an actual value of the Q-function over the policy π, and Qθ (s, a) is the estimated value of the Q-function given the vector of weightings θ . Note that, differently from the steady state distribution π, the probability distribution Z expresses the 10 Mar 2017 at 08:08:07, .007

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frequency of revisiting a state–action pair. In other words, the probability distribution Z describes how often a state-action pair is revisited. However, computation of the MSE is intractable for systems with large state spaces. Thus, we can find a local minimum for the MSE by using the stochastic gradient descent (SGD) method.1 The SGD method allows us to calculate the updated value of θ  by following an approximation of the gradient of the error function. Specifically, a learning rate factor α will be used to adjust the step size of the SGD method and prevent overshooting. Then, we can update the weighting vector θ in the direction of the gradient as follows: 1 θ t+1 = θ t − αt ∇θ t ζ (θθ t ), 2 % $  = θ t + αt EZ Qπ (s, a) − Qθ t (s, a) ∇Qθ t (s, a) . (6.17)  In (6.17), to compute the second term, EZ [(Qπ (s, a)−Qθ t (s, a) ∇Qθ t (s, a)], we need to know the probability distribution Z, which may not be possible in practice. This leads to the idea of adopting the bootstrapping method [22, 23] for estimating the second term. Bootstrapping is a statistical method designed with the main aim of deriving robust estimates for standard errors by sampling the original sample and then estimating the sampling distribution. Now, instead of calculating over the whole distribution Z, we can update the value of θ at each sample gradient as follows:   (6.18) θ t+1 = θ t + αt Qπ (st , at ) − Qθ t (st , at ) ∇Qθ t (st , at ). Since each sample gradient is an unbiased estimate of the true gradient, this converges to a local minimum of the MSE if the step size α decreases appropriately with t, e.g., α satisfies Assumption 1 [21]. In (6.18), by using the Q-value approximation function in (6.15), we derive the following result:   (6.19) θ t+1 = θ t + αt Qπ (st , at ) − Qθ t (st , at ) φ (st , at ). We are now ready to present an online learning algorithm with a linear function approximation for the gateway of the WPBAN as in Algorithm 6.3. In Algorithm 6.3, κt denotes the temporal difference which is used to adapt the prediction for the agent by comparing the Q-value at the current state and the prediction at the next state. The vector e denotes the approximation of the gradient ∇θ Qθ (s, a). We then introduce the following theorem. theorem 6.2. Let the learning policy πθ be an -greedy policy with respect to θ and let C be the Lipschitz constant of the learning policy πθ with respect to θ . In addition, we assume that Assumption 1 is satisfied. Then, there is C0 > 0 such that, if C < C0 , Algorithm 6.3 converges with probability one. The proof of Theorem 6.2 is provided in Section 6.5. 1 Gradient methods for minimizing the MSE are commonly used in the literature, especially in machine

learning. More information on using gradient methods can be found in [21].

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Algorithm 6.3 SARSA with linear function approximation   Input. Initialize a set of features φ  (s, a) = φ1 · · · φf · · · φF along with arbitrary weights θ  = θ1 · · · θf · · · θF with the same dimensionality F as the feature vector φ . For each state–action pair (s, a), initialize the table entry Q(s, a) arbitrarily, e.g., to zero. Observe the current state s, initialize the learning rate α and the discount factor γ . for t := 1 to T do From the current state–action pair (s, a), execute action a and obtain the immediate reward r and a new state s . Select an action a from As using a policy derived from Q-learning policy, e.g., -greedy. Then, let e t = φ (s, a),

(6.20) 



κt = r(s, a) + γ Qθ t (s , a ) − Q(s, a).

(6.21)

Then, the weights are updated as follows: θ t+1 = θ t + αt κte t . Replace s ← end for

s

and a ←

(6.22)

a .

remark 2. Algorithm 6.3 is straightforward to implement for the gateway. It just requires a small amount of the gateway’s memory to store the parameters with very simple computations at each time step to update the parameters. However, one of the challenges in Algorithm 6.3 is to find appropriate features for the linear function approximation. The features chosen must not only indicate the best action to execute, but also convey information about what future states are useful. For example, in our proposed system, we aim to minimize the average delay and the packet loss for packets (especially for important packets) in the system. Therefore, we need to have features for different types of packets at different sensors. One example is given in (6.23) below for the performance evaluation. Further discussions on building features for the linear function approximation can be found in [21, 24, 25].

6.2.5

Performance Evaluation

6.2.5.1

Parameter Setting We perform the simulations using MATLAB to evaluate the performance of the proposed learning algorithm, i.e., Algorithm 6.3 under different parameter settings. First, we consider the case with two sensor nodes. The packet arrival probabilities of sensor nodes 1 and 2 are 0.5 and 0.4, respectively. Here 30% and 20% of the packets arriving at sensor nodes 1 and 2 are important packets, respectively. The maximum data queue size of both nodes is five packets. We assume that node 1 has higher priority than that of 10 Mar 2017 at 08:08:07, .007

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node 2, and thus the priority factors are set to 1.3 and 1, respectively. Furthermore, the probabilities that nodes 1 and 2 are near to the gateway are 0.7 and 0.9, respectively. The weighting of the important packet is 1.5 and that of the normal packet is 1. For the gateway, we assume that the maximum energy buffer size is 10 units of energy. The gateway uses 1 unit and 2 units of energy to transfer wireless energy and collect data when the sensor node is near and far, respectively. The probability of the gateway visiting the charger is 0.6. The probability that the gateway can harvest 1 unit or 2 units of energy from the charger is 0.5. The parameters of the learning algorithm are set as follows. The discount factor is 0.98, and the exploration parameter is 0.01. For the feature function, one of the most effective ways is to find key features on the basis of the objective function. In our proposed system, the objective function is the cost defined in (6.6). From (6.6), the feature function can be defined as follows: Qθ (s, a) =

N 

θni φni (s, a) + θnm φnm (s, a),

(6.23)

n=1

where N is the number of sensor nodes and in our case N = 2. Here φnx (n = 1, . . . , N) are numerical features corresponding to the types of packets of the nodes, and θnx are the weightings of such features. Here, x = i and x = m correspond to the cases of an important packet and a normal packet, respectively. We choose an initial arbitrary weight of 5, i.e., θnx = 5. The actions of the gateway that affect the feature functions can be defined as follows. •

Action = “charging” – –

•

Action = “do nothing” –

•

φnx = −(σn δ x + (1 − cn ))1(dnx ), where 1(y) = 0 if y = 0 and 1(y) = 1 if y>0

Action = “accept one important packet from node n” – –

•

if dnx = 0: φnx = σn δ x if dnx > 0: φnx = (−e/E)σn δ x + (1 − cn )

φni = σn δ i + (2 − cn ) and φnm = 0 φnx = −σn δ x 1(dnx ) (where n represents nodes other than node n)

Action = “accept one normal packet from node n” – –

φnm = σn δ m + (2 − cn ) and φni = 0 φnx = −σn δ x 1(dnx )

We consider the case that the sensor nodes and gateway have no information about the environment, e.g., the probabilities that a node is near the gateway and the gateway visits a charger. Therefore, to compare and evaluate the performance of the proposed learning algorithm, we consider two baseline schemes, i.e., a greedy-myopic (GM) policy and a 10 Mar 2017 at 08:08:07, .007

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charging-myopic (CM) policy. For the GM policy, the gateway always takes the action “transmit” as long as it has enough energy. For the CM policy, the gateway always takes the action “charging” when it visits a charger, and it always takes the action “transmit” if it has enough energy and does not visit the charger. For both baseline schemes, when the action “transmit” is taken, the gateway will select an important packet if there is one from the node that minimizes the cost function C as given in (6.6).

6.2.5.2

Simulation Results We first evaluate the performance of the proposed learning algorithm with the linear function approximation defined in (6.23) by analyzing the convergence results and the policy obtained. We then vary the charger visit probability of the gateway and the priority factor of sensor node 1 to show the efficiency of the proposed learning algorithm compared with the GC policy and the GM policy. Additionally, to gain more insight, we present results obtained by the learning algorithm with the linear function approximation defined by Qθ (s, a) = θg φg (s, a) +

N 

θni φni (s, a) + θnm φnm (s, a).

(6.24)

n=1

In (6.24), we define a new feature, denoted by φg , together with its weighting θg , the aim of which is to show that, by defining more specific feature for the system, we can obtain better performance. The feature θg can be expressed as the feature of energy levels of the gateway, and it can be defined as follows:  1 − e/E, if action = “charging,” φg = (6.25) 0, otherwise. Note that we denote the linear function approximations defined in (6.23) and (6.24) as feature function 1 and feature function 2, respectively.

Convergence and Policy We first show the convergence and the optimal policy obtained by the proposed algorithm, i.e., Algorithm 6.3. The convergence in terms of the average cost is shown in Figure 6.9(a), and the weights of the feature function is shown in Figure 6.9(b). The convergence rates of the weightings of the feature function are relatively fast, with around 4 × 103 iterations, while the convergence of the average cost of the proposed learning is slightly slower, with around 4 × 105 iterations. This is because the average cost converges only after the weightings have converged. In particular, in the first 104 iterations, the average cost of the learning algorithm increases to 9.5. Then, in the next 105 iterations, it reduces gradually and becomes stable at 8.35 after 4 × 105 iterations. Although the convergence rate of the learning algorithm is relatively slower than those of the GM and CM policies, the average cost obtained by the proposed learning algorithm is much lower, i.e., 8.35 versus 10.6686 and 10.2254, respectively. After the converged weightings have been reached for the learning algorithm, we obtain the policy through Algorithm 6.3 with the Q-function from (6.23). Next, we 10 Mar 2017 at 08:08:07, .007

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(a)

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GC policy

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Figure 6.9 The convergence of (a) the average cost of the system and (b) the parameters of

weightings in the feature function. (a)

(b)

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–25

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Figure 6.10 The Q-value functions of (a) node 1 far and node 2 far, (b) node 1 far and node 2

near, (c) node 1 near and node 2 far, and (d) node 1 near and node 2 near to the gateway.

evaluate the common scenarios, i.e., when both nodes have both important and normal packets in the data queue. We analyze the impact of the energy and distance state from the nodes to the gateway to the policy. In particular, in Figure 6.10, we consider four cases, i.e., when both nodes are far from the gateway (Figure 6.10(a)), when node 1 is far from and node 2 is near to the gateway (Figure 6.10(b)), when node 1 is near to and node 2 is far from the gateway (Figure 6.10(c)), and when both nodes are near to the gateway (Figure 6.10(d)). In these figures, the Q-values of different actions are shown, 10 Mar 2017 at 08:08:07, .007

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(c)

(b)

(a) Doing nothing 0%

Transmitting 52%

Charging 48%

Transmitting 45%

Doing nothing 22%

Charging 33%

Doing nothing 1% Charging 40% Transmitting 59%

Figure 6.11 The percentages of different actions obtained by employing (a) the GC policy, (b) the GM policy, and (c) the learning algorithm.

and the gateway will choose the action that has the highest Q-value. In Figure 6.10(a), when both nodes are far from the gateway, the gateway will take the action “charging” to reserve energy for future transmissions. However, when both nodes are near to the gateway, i.e., Figure 6.10(d), the gateway only takes the action “charging” when the energy level is lower than 2 units. The gateway will select node 1 for data transmission if the current energy level is higher than 1 unit. When one node is closer to the gateway, the gateway will choose the near node for data transmission if the energy level is greater than or equal to 2 units. In Figure 6.11, we compare the percentages of the different actions taken by the gateway. As shown in Figure 6.11, by adopting the learning algorithm, the gateway is able to balance between the actions “charging” and “transmitting” while the occurrence of the action “do nothing” is minimized. With enough energy, the learning algorithm is able to take the action “transmitting” more frequently than occurs in the baseline schemes, resulting in higher throughput. In particular, the charging rate of the learning algorithm is 40%, which is lower than that of the GC policy, i.e., 48%. However, the data transmitting rate of the learning algorithm is higher than that of the GC policy, 59% versus 52%.

Average Cost and Energy In the aforementioned analysis, the most important factor influencing the learning policy is the energy of the gateway. The energy is limited, and thus the gateway has to balance between taking charging action and the data transmission action. To obtain more insight, in Figure 6.12, we vary the charger visit probability from 0.1 to 0.9 and compare the average cost (Figure 6.12(a)) and the average available energy of the gateway (Figure 6.12(b)). As shown in Figure 6.12(a), as the charger visit probability increases from 0.1 to 0.5, the average costs of the GM policy, the GC policy, and the learning algorithms decrease gradually to 11, 10.2, and 8.9, respectively. However, as the charger visit probability increases from 0.5 to 0.9, the average costs of the GM policy and the learning algorithms keep decreasing while that of the GC policy slightly increases. When the charger visit probability is 0.9, the average cost of the learning algorithm becomes 7.8, which is lower than those of the GM and GC policies, around 22% and 27%, respectively. The reason for the cost increment of the GM policy is that, when the charger visit probability is high, the amount of energy received is more than that 10 Mar 2017 at 08:08:07, .007

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(b)

(a)

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16 Greedy-Myopic (GM) Policy Greedy-Charging (GC) Policy Learning Algorithm with feature function 1 Learning Algorithm with feature function 2

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Greedy-Myopic (GM) Policy Greedy-Charging (GC) Policy Learning Algorithm with feature function 1 Learning Algorithm with feature function 2

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0.4

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Charger visit probability

Figure 6.12 (a) The average cost of the system and (b) the average available energy of the gateway when the charger visit probability is varied.

required since the GM policy always takes “charging” action as shown in Figure 6.11. For the learning algorithms, although the available energy of the gateway is not as high as for the GM policy, the algorithm is able to balance between energy receiving and data transmission so that the best performance can be achieved (as shown in Figure 6.11). Consequently, we observe that the average energy of the learning algorithms falls in between those of the GM and GC policies as shown in Figure 6.12(b). Furthermore, when the charger visit probability is not high, the average cost obtained by the learning algorithm with feature function 2 is slightly lower than that of the learning algorithm with feature function 1. This reveals that the gateway can reserve more energy to achieve better performance when the energy is scarce.

Average Packet Loss Next, we examine the impact of the available energy on the packet loss probability and the average number of packets waiting in the data queues. In the system under consideration, the average loss of important packets is always kept at a very small level. Specifically, when the charger visit probability is 0.1, the packet loss probability for important packets of all four algorithms is relatively high, i.e., around 10% due to the lack of enough energy. However, this probability drops dramatically to around 3% when the charger visit probability is 0.2 and is approximately zero when the charger visit probability is higher than 0.2. This result clearly shows that the important packets are well prioritized. However, normal packets can experience a high packet loss probability. This is enforced in order to yield a transmission opportunity to the important packets. In particular, when the charger visit probability is low, i.e., 0.1, the packet loss probability of the normal packets is very high (around 67%), and this probability decreases as the charger visit probability increases for the GM policy and the learning algorithm. For the GC policy, because it spends too much time for charging, when the gateway visits the charger more frequently, the time for data transmission reduces. Consequently, the aver10 Mar 2017 at 08:08:07, .007

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(b)

(a) 0.12

0.7 Greedy-Myopic (GM) Policy Greedy-Charging (GC) Policy Learning Algorithm with feature function 1 Learning Algorithm with feature function 2

0.1

Greedy-Myopic (GM) Policy Greedy-Charging (GC) Policy Learning Algorithm with feature function 1 Learning Algorithm with feature function 2

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Figure 6.13 The average loss of (a) important packets and (b) normal packets in the system.

age packet loss becomes worse. For all cases, the learning algorithm always achieves the best performance in terms of minimizing the packet loss as shown in Figure 6.13. We now examine the impact of the priority factor on the average packet loss. In particular, we fix the charger visit probability at 0.6, keep the priority factor of node 2 at 1, and vary the priority factor of node 1 from 0.2 to 1.8. As the priority factor of node 1 increases, the average packet losses of node 1 obtained by the GC and GM policies have a downward trend, while those of node 2 have an upward trend, as shown in Figures 6.14(a), (b), (d), and (e). This implies that the node with the higher priority factor has more opportunities to transmit data, and thus its average packet loss will be lower. Similar trends are observed for the average packet losses of node 1 and node 2 obtained by the learning algorithm. However, when the value of the priority factor of node 1 is close to 1.0, i.e., the value of the priority factor of node 2, the average normal packet losses of node 1 and node 2 fluctuate. The reason is that, when the priority factors of the two nodes are close to each other, the learning algorithm can choose randomly one of the nodes to transmit data as long as the cost function is minimized. Thus, the average packet loss of normal packets obtained by the learning algorithm for the whole system is much lower than those of the GP and GM policies as shown in Figure 6.14(f). Through this result, we are able to set the priority factors of the nodes to achieve performance requirements.

6.3

Future Research Directions There are some research directions which we can study regarding this topic. •

Energy tradeoff for wireless backscattering nodes. The backscattering nodes need to control and balance the time allocated to harvesting energy and the time allocated to backscattering of signals. If the system spends too much time on the energy harvesting process, the backscatter node will have less chance to transmit data to its destination, whereas if too much time is spent on the backscattering 10 Mar 2017 at 08:08:07, .007

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(b) Average important packet loss node 1

0.05 0.04 0.03 0.02 0.01 0.4

0.6 0.8 1 1.2 1.4 1.6 1.8 Priority factor node 1 The average packet loss of important packets node 1

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(f) Greedy-Myopic (GM) Policy Greedy-Charging (GC) Policy Learning Algorithm with feature function 1 Learning Algorithm with feature function 2

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Greedy-Myopic (GM) Policy Greedy-Charging (GC) Policy Learning Algorithm with feature function 1 Learning Algorithm with feature function 2

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Figure 6.14 The average packet loss when the priority factor of node 1 is varied.

•

6.4

process, the backscatter node may not have sufficient energy for its remaining operations. Therefore, depending on the specific environmental conditions, the backscatter node needs to take optimal decisions through optimization frameworks such as MDPs or learning algorithms in order to adapt to the dynamic of the environment. Integrating backscattering communication and other wireless networks. Recently, the development of ambient backscattering communication systems has overcome the limitations of conventional backscattering communication systems by using ambient signals. Ambient signals, e.g., TV or radio signals, can be harvested or scatted from many sources, e.g., TV towers and access points. However, to harvest and scatter such signals efficiently without having harmful impacts on other wireless communication systems, cooperation models and joint optimization solutions under constraints need to be taken into account.

Summary The development of wireless energy harvesting techniques together with backscattering communication has opened new opportunities for wireless communications systems. In particular, for new wireless communication systems, wireless nodes can adopt backscattering techniques to transmit signals, besides using traditional methods. Furthermore, 10 Mar 2017 at 08:08:07, .007

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with the improvement of wireless energy harvesting techniques, backscattering communication systems can overcome inherent limitations, e.g., for wireless tag readers there will be no need to transmit signals to the wireless tag. In this chapter, we first presented some fundamental background of backscattering techniques and then we discussed some applications of wireless energy harvesting techniques in backscattering communication systems. After that, we introduced an application of a backscattering technique together with magnetic resonance coupling in a wireless body sensor network with the aim of minimizing the total cost of the system. Simulation results have demonstrated the efficiency of the proposed solutions as well as the potential benefits of backscattering and wireless energy harvesting techniques. Finally, we have highlighted some future research directions in this topic.

6.5

Appendix To prove Theorem 6.2, we adopt the ordinary differential equations (ODE) approach. From (6.22), we can re-write the update for the weighting parameters as follows:   θ t+1 = θ t + αtφ (s, a) r(s, a) + γ Qθ t (s , a ) − Q(s, a) . (6.26) Recall that the standard Euler scheme for numerically approximating a trajectory of the ODE x˙ = h(x(t)) would be xn+1 = xn + αt h(xn ) (see Chapter 2 of [26]). Then, from (6.15), (6.17), (6.18), and (6.26), the associated ODE of θ can be expressed as follows: $ %  θ˙ = Eθ φ (s, a) r(s, a) + γ Qθ (s , a ) − Q(s, a) , $ %  (6.27) = Eθ φ (s, a) r(s, a) + γ φ  (s , a )θθ − φ  (s, a)θθ . In (6.27), we omit the dependence of θ on t for presentation convenience. Now, we will follow Theorem 17 from [27] and show that, if the associated ODE of θ has a globally asymptotically stable equilibrium point, Algorithm 6.3 will converge with probability one. To determine the global asymptotic stability for the associated ODE of θ , we rewrite (6.27) in the following form: (6.28) θ˙ = Aθ θ + bθ ,     φ (s, a) . where Aθ = Eθ φ (s, a)(γ φ  (s , a ) − φ  (s, a)) and bθ = Eθ r(s, a)φ θ (t) = θ (t) −θθ ∗ . Then, from the Denote θ ∗ as the equilibrium point of (6.28)2 and let  Lyapunov stability theory, we have the following statement. Given the ODE x˙ = f (x), if there exists a function V(x) : Rn → R such that V(x = 0) = 0, V(x) > 0 (∀x = 0), V(x) → ∞ as x → ∞, 2 The existence of such an equilibrium point was proved in [28].

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(6.29)

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˙ then, if V(x) < 0 (∀x = 0), the ODE x˙ = f (x) is globally asymptotically stable. Now, letting x =  θ and V(x) =  θ 22 , it is straightforward to verify the conditions of  ˙  V(θ ) in (6.29). Hence, if we can prove that V( θ ) < 0, then the ODE (6.28) is globally asymptotically stable. We derive the following results: d 2  d θ θ 2 = 2 θ dt dt   d = 2 θ θ (t) − θ ∗ dt   = 2θ (Aθ θ − Aθ ∗ θ ∗ + bθ − bθ ∗ )  θ ) + bθ − bθ ∗ ) = 2 θ (Aθ θ − Aθ ∗ (θθ −  





θ (bbθ − bθ ∗ ) θ + 2 θ (Aθ − Aθ ∗ )θθ + 2 = 2 θ Aθ ∗ A θ 2 bbθ − bθ ∗ 2 θ + 2 θ 2 (Aθ − Aθ ∗ )θθ 2 + 2 θ θ ∗ ≤ 2 

≤ 2 θ Aθ ∗ θ + 2 θ 2 sup Aθ − Aθ ∗ 2 θθ 2 + 2 sup

θ =θ ∗

θ 

≤ 2 θ Aθ ∗ θ + ϑ θ 22 sup Aθ − Aθ ∗ 2 + 2 sup

θ =θ ∗

θ

bbθ − bθ ∗ 2  2 θ 2 , θθ − θ ∗ 2

bbθ − bθ ∗ 2  2 θ 2 , θθ − θ ∗ 2 (6.30)

where ϑ is a positive small constant. Then, let λA = sup Aθ − Aθ ∗ 2 , θ

λB = sup

θ =θ ∗

bbθ − bθ ∗ 2 θθ − θ ∗ 2

(6.31)

where λA is the operator norm (induced form) and λB is the operator norm corresponding to the 2-norm for vectors, i.e., the regular Euclidean norm [29]. Then, we derive the following results:   ϑ d 2    (6.32) θ 2 ≤ 2θ Aθ ∗ θ + 2 λA + λB  θ 22 . dt 2 Denoting λ = (ϑ/2)λA + λB , we have d 2  θ (Aθ ∗ + λI) θ. θ 2 ≤ 2 dt

(6.33)

As stated in Theorem 6.2, because the learning policy is assumed to be a Lipschitz constant with regard to the vector θ and the corresponding induced chain has a uniform ergodicity feature, Aθ and bθ are also Lipschitz constant with regard to the vector θ . This implies that λA and λB → C. Additionally, from Theorem 1 of [30], we have that Aθ is a negative definite matrix. Therefore, given a sufficiently small value of C, (Aθ ∗ + λI) is a negative definite matrix. Consequently, the ODE in (6.28) is globally asymptotically stable. The proof has been completed. 10 Mar 2017 at 08:08:07, .007

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References [1] H. Stockman, “Communication by means of reflected power’,’ in Proceedings of the IRE, vol. 36, no. 10, pp. 1196–1204, October 1948. [2] C. Boyer and S. Roy, “Backscatter communication and RFID: Coding, energy, and MIMO analysis,” IEEE Transactions on Communications, vol. 62, no. 3, pp. 770–785, March 2014. [3] V. Liu, A. Parks, V. Talla et al., “Ambient backscatter: Wireless communication out of thin air,” ACM SIGCOMM Computer Communication Review, vol. 43, no. 4, pp. 39–50, October 2013. [4] B. Kellogg, A. Parks, S. Gollakota, J. R. Smith, and D. Wetherall, “Ambient backscatter: Wireless communication out of thin air,” in Proc. 2014 ACM conference on SIGCOMM, August 2014, pp. 607–618. [5] R. Correia, N. B. D. Carvalho, G. Fukuda, A. Miyaji, and S. Kawasaki, “Backscatter wireless sensor network with WPT capabilities,” in IEEE MTT-S International Microwave Symposium, May 2015, pp. 1–4. [6] G. Yang, C. K. Ho, and Y. L. Guan, “Multi-antenna wireless energy transfer for backscatter communication systems,” IEEE Journal on Selected Areas in Communications, vol. 33, no. 12, pp. 2974–2987, November 2015. [7] A. S. Boaventura and N. B. Carvalho, “Evaluation of simultaneous wireless power transfer and backscattering data communication through multisine signals,” in IEEE Wireless Power Transfer Conference, May 2015, pp. 1–3. [8] A. Collado and A. Georgiadis, “Improving wireless power transmission efficiency using chaotic waveform,” in IEEE MTT-S International Microwave Symposium Digest, June 2012, pp. 1–3. [9] K. Finkenzeller, RFID Handbook: Fundamentals and Applications in Contactless Smart Cards, Radio Frequency Identification and Near-Field Communication, 3rd edn. West Sussex: Wiley, 2010. [10] J. D. Griffin, High-Frequency Modulated-Backscatter Communication Using Multiple Antennas, PhD Thesis, School of Electrical and Computer Engineering, May, 2009. [11] S. Movassaghi, M. Abolhasan, J. Lipman, D. Smith, and A. Jamalipour, “Wireless body area networks: A survey,” IEEE Communications Surveys & Tutorials, vol. 16, no. 3, pp. 1658–1686, January 2014. [12] R. Cavallari, F. Martelli, R. Rosini, C. Buratti, and R. Verdone, “A survey on wireless body area networks: Technologies and design challenges,” IEEE Communications Surveys & Tutorials, vol. 16, no. 3, pp. 1635–1657, February 2014. [13] S. Basagni, M. Y. Naderi, C. Petrioli, and D. Spenza, “Wireless sensor networks with energy harvesting,” in Mobile Ad Hoc Networking: Cutting Edge Directions, 2nd edn., Hoboken, NJ: Wiley. [14] S. D. Barman, A. W. Reza, N. Kumar, M. E. Karim, and A. B. Munir, “Wireless powering by magnetic resonant coupling: Recent trends in wireless power transfer system and its applications,” Renewable and Sustainable Energy Reviews, vol. 51, pp. 1525–1552, November 2015. [15] X. Lu, P. Wang, D. Niyato, D. Kim, and Z. Han, “Wireless charging technologies: Fundamentals, standards, and network applications,” IEEE Communications Surveys & Tutorials, vol. 18, no. 2, pp. 1413–1452, second quarter, 2016. 10 Mar 2017 at 08:08:07, .007

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[16] A. P. Sample, D. A. Meyer, and J. R. Smith, “Analysis, experimental results, and range adaption of magnetically coupled resonators for wireless power transfer,” IEEE Transactions on Industrial Electronics, vol. 58, no. 2, pp. 544–554, February 2011. [17] M. Akimoto and M. Iizuka, “Load modulation applied to magnetic resonance wireless power transfer technology and its applications,” NTT Technical Review, vol. 11, no. 10, not paginated, October 2013. [18] W. Dabney, Adaptive Step-Sizes for Reinforcement Learning, Doctoral Dissertation, May 2014. [19] C. J. C. H. Watkins and P. Dayan, “Q-Learning,” Machine Learning, vol. 8, nos. 3–4, pp. 279–292, 1992. [20] S. Singh, T. Jaakkola, M. L. Littman, and C. Szepesvari, “Convergence results for singlestep on-policy reinforcement-learning algorithms,” Machine Learning, vol. 38, no. 3, pp. 287–308, 2000. [21] R. S. Sutton, and A. G. Barto. Reinforcement Learning: An Introduction, vol. 1. Cambridge, MA: MIT Press, 1998. [22] B. Efron, “Bootstrap methods: Another look at the jackknife,” The Annals of Statistics, vol. 7, no. 1, pp. 1–26, 1979. [23] M. Geist and O. Pietquin, “A brief survey of parametric value function approximation,” technical report, September 2010. [24] A. Geramifard, T. J. Walsh, S. Tellex et al., “A tutorial on linear function approximation for dynamic programming and reinforcement learning,” Foundations and Trends in Machine Learning, vol. 6, no. 4, pp. 375–451, 2013. [25] J. N. Tsitsiklis and B. V. Roy, “Feature-based methods for large scale dynamic programming,” Machine Learning, vol. 22, no. 1-3, pp. 59–94, March 1996. [26] J. C. Butcher, The Numerical Methods for Ordinary Differential Equations, Hoboken, NJ: Wiley, 2008. [27] A. Benveniste, M. Metivier, and P. Priouret, Adaptive Algorithms and Stochastic Approximations. Berlin: Springer, 1990. [28] D. P. De Farias and B. V. Roy, “On the existence of fixed points for approximate value iteration and temporal-difference learning,” Journal of Optimization Theory and Applications, vol. 105, no. 3, pp. 589–608, June 2000. [29] G. H. Golub and C. F. V. Loan, Matrix Computations. Baltimore, MD: Johns Hopkins University Press, 1996. [30] J. N. Tsitsiklis and B. V. Roy, “An analysis of temporal-difference learning with linear function approximation,” IEEE Transactions on Automatic Control, vol. 42, no. 5, pp. 674– 690, May 1997.

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7

Dedicated Wireless Energy Harvesting in Cellular Networks: Performance Modeling and Analysis Hina Tabassum and Ekram Hossain

7.1

Introduction Energy harvesting in wireless cellular networks is a cornerstone of emerging 5G and beyond 5G (B5G) cellular networks as it aims to “cut the last wires” of the existing wireless devices [1]. In particular, energy harvesting has a significant potential to attract subscribers since it promotes mobility and connectivity anywhere and anytime, which is one of the key visions of next-generation wireless networks. In general, wireless energy harvesting can be classified according to the following two categories. •

•

Ambient energy harvesting (EH). This refers to energy harvested from renewable energy sources (such as thermal, solar, wind, etc.) as well as energy harvested from radio signals of different frequencies in the environment that can be sensed by EH receivers (e.g., co-channel interference, TV or radio broadcasting, etc.). Dedicated EH. This enables the intentional transmission of energy from dedicated energy sources to energy harvesting devices.

To satisfy the power demands of delay-constrained wireless applications, it is of utmost importance to ensure the availability of sufficient energy at the user terminals whenever required. This fact has motivated researchers toward the development of dedicated wireless-powered cellular networks (WPCNs) where dedicated energy sources or hybrid access points (HAPs) take care of both energy transfer and information transmission to and from the subscribers. In this chapter, we focus on dedicated EH techniques. We first highlight the associated challenges. Next, we theoretically characterize and comparatively analyze a number of different network architectures for centralized and distributed dedicated wireless EH. Numerical results are provided to validate the analytical results.

Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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Major Challenges in Dedicated Wireless Energy Harvesting In this section, we will discuss a number of major challenges related to dedicated wireless energy harvesting (WEH) from the perspective of network architecture and modeling and resource allocation.

7.2.1

Network Architectures for Wireless Energy Harvesting Different network architectures have been studied for WEH. However, most of the studies have been limited to a two- or three-node network model, a central base station (BS) that takes care of both the wireless information transmission and energy transfer, and follows a specific configuration of energy harvesting; i.e., a user harvests energy from a centralized half-duplex BS or full-duplex BS or through randomly deployed power beacons (PBs), etc. However, a comparative performance analysis of different WPCN configurations needs to be conducted, which can potentially reveal insights related to their feasibility in various network scenarios. For instance, in the case of full-duplex BSs, the self-interference (SI) from the transmitter of the BS to its co-located receiver is a fundamental bottleneck that can cause significant deterioration of the information reception at the BS [2]. To overcome SI, complex and efficient SI cancellation schemes are required. Also, SI cancellation at a BS with a high transmit power can be very costly. Therefore, it is important to analyze the advantages of implementing full-duplex BS over other low-cost WPCN configurations with traditional half-duplex BS.

7.2.2

Doubly Near–Far Problem in Energy Harvesting Cellular Networks Owing to distance-dependent signal attenuation both in the uplink and in the downlink, any user located closer to a HAP harvests more energy in the downlink and also requires less power to attain a given signal-to-noise ratio (SNR) at the HAP in the uplink (given a fixed transmission and energy harvesting time slot). On the other hand, distant users harvest smaller amounts of energy in the downlink but require higher transmission power to achieve the same SNR in the uplink. This situation is typically referred to as the “doubly near–far problem” in the literature [3]. This phenomenon may reduce the fairness among different users that are located spatially apart (e.g., cell-centre and cell-edge users) from the HAP. However, this is an interference-free perspective of the doubly near–far problem that does not consider the interference experienced by cell-edge users. In practice, a macrocell is surrounded by several tiers of neighboring macrocells. Therefore, cell-edge users are typically exposed to higher interference levels and may accumulate higher amounts of energy (e.g., by ambient RF energy harvesting) than cell-centre users.

7.2.3

Additional Resource Consumption at HAPs HAPs are responsible for energy transfer in order to support both uplink and downlink transmissions. With this obligation, a HAP is typically assumed to allocate a specific 10 Mar 2017 at 08:08:00, .008

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portion of time, power, channels, or antennas for energy transfer. Note that the simultaneous use of a channel (or resource) for optimized downlink wireless information transfer (WIT) in addition to wireless energy transfer (WET) for uplink transmission has not been considered in recent studies [3, 4]. This additional resource consumption at HAP is particularly significant for uplink transmission scenarios. In conventional uplink cellular networks, the maximum power consumption of a wireless device is relatively low compared with that of a BS. In contrast, WPCNs consume extra time/power resources due to HAPs, especially for uplink transmissions of far-away users. This fact triggers an asymmetric additional power consumption, which is not the case in traditional cellular networks. We refer to this phenomenon as asymmetric power consumption in uplink.

7.2.4

Multiuser Scheduling in WPCNs Conventional uplink multiuser scheduling schemes (e.g., greedy/opportunistic scheduling, round-robin scheduling) do not consider the amount of energy harvested and/or energy requirements of the selected users, and therefore, when used in WPCNs, they can lead to • •

energy (or transmit power) outages, in which the harvested energy of a scheduled user drops below the minimum energy (or power) required for transmission, and energy overflows, in which the harvested energy of a scheduled user exceeds its finite battery level (and hence energy is wasted at the HAP for wireless charging).

Energy outage and energy overflow events mainly occur, respectively, when cell-centre and cell-edge users are scheduled for transmission. Note that traditional uplink scheduling methods such as the greedy scheduling method generally consider uplink channel state information (CSI) only, whereas round-robin scheduling chooses any user with equal probability regardless of her channel conditions. Therefore, energy outage events may affect fairness-constrained scheduling schemes (e.g., a round-robin scheduling scheme) significantly more than they affect opportunistic (i.e., channel state-aware) scheduling schemes, due to the higher chances of scheduling of cell-edge users. New scheduling methods and performance metrics such as the spectral efficiency of uplink transmission and spectral efficiency per unit of charging power will be required.

7.2.5

On Request Energy Transfer/Cease Protocols WPCNs rely mainly on a centralized entity (such as a HAP), which coordinates both WET and WIT. Depending on the objectives of network operators (e.g., throughput maximization [3]), a specific duration is reserved for the users for energy harvesting. Nevertheless, these users may accumulate sufficient energy from ambient RF sources as well. Therefore, it will be crucial to design light-weight protocols that allow communication between the HAP and harvesting devices (e.g., to request more energy from the HAP in the case of on impending SNR outage or inform the HAP in cases which sufficient energy has been accumulated beforehand). This will reduce unnecessary resource 10 Mar 2017 at 08:08:00, .008

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WPCN Configuration 1

249

WPCN Configuration 2 Power Beacon

Full-Duplex BS

U3

Half-Duplex BS

U3

R

U1

U1

r U2

U2 T

BS or PBs

t U1

t t U2

U3

Downlink Energy Transfer Uplink Information Transfer

Tframe Figure 7.1 Graphical illustration of the WPCN configurations considered and the time frame

structure for uplink information and downlink energy transfer. In configuration 1, users harvest energy from and transfer information to a full-duplex BS. In configuration 2, users harvest energy from PBs and transfer information to a conventional half-duplex BS.

consumption at the HAP that may lead to energy overflow at the harvesting devices. In addition, these protocols may also enable users to request additional energy from on-request dedicated power resources (e.g., PBs as shown in Figure 7.1), if such are available.

7.2.6

Coordination among HAPs on Uplink Channels Coordination among HAPs is a desirable feature of emerging WPCNs. The definition of coordination among HAPs (especially for uplink transmissions) needs to be rethought and modified. Note that, if all of the HAPs coordinate and synchronize their energy transfer phases, it will help cell-edge users to accumulate higher energy levels. On the other hand, their coordination during the uplink transmission phase will mitigate strong interference received at a HAP from neighboring HAPs, since the users in other cells, rather than the HAPs, will be transmitting. This fact calls for optimizing the energy and information transfer time during which all HAPs can coordinate to maximize their mutual benefits on uplink transmission channels (i.e., accumulation of energy for celledge users in the downlink and interference mitigation at HAPs in the uplink). Note that adapting the energy harvesting duration (according to the channel conditions of the users) at all HAPs in a distributed fashion (e.g., [3] and other follow-up studies) does not allow coordination among HAPs. Thus, cell-edge users may lose the benefits 10 Mar 2017 at 08:08:00, .008

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of interference from other HAPs during WET, and HAP will be exposed to higher interference (i.e., interference from nearby HAPs) during the uplink WIT. Hence, to promote synchronization and coordination among HAPs, the durations of WET and WIT need be optimized jointly by all HAPs.

7.3

Centralized and Decentralized Dedicated WEH Architectures: Comparative Analysis This section presents a mathematical framework [5] that captures the channel diversity of multiple harvesting devices, characterizes the SNR outage zone, proposes improved WPCN configurations (compared with the existing ones), and comparatively analyzes the performances of the proposed and existing WPCN configurations. In particular, we characterize the SNR outage zone as a function of system parameters considering halfduplex and full-duplex BS configurations. These BS configurations are considered as a baseline to analyze the relative performance gains of the proposed configurations. We then propose a symmetric1 deployment of low-cost PBs around the half-duplex BS in which a user harvests energy from the PBs and transfers information to a conventional half-duplex BS. The performance gains are shown over the full-duplex BS and random deployment of the PBs in a WPCN. We characterize the SNR outage probability and spectral efficiency of an arbitrarily located user in the uplink. In the proposed WPCN configuration, we optimize the distance away of the PBs to minimize the SNR outage probability and provide closed-form solutions for special cases. Numerical results provide a comparative performance analysis of the configurations listed, validate the expressions derived, and reveal the significance of the optimal deployment of a limited number of PBs rather than a large number of PBs deployed randomly or full-duplex BS.

7.3.1

System Model We consider a circular macrocell of radius R with a BS powered from a fixed energy source located in the cell centre. The macrocell considered is overlaid with M PBs and has U users that are uniformly distributed within the macrocell coverage area. Each user is equipped with an antenna that can either transmit information or receive energy at a given time. All users transmit to the BS for a predefined duration τ in a sequential manner. In order to guarantee strict resource fairness among users, the total length of a time frame is given as Tframe = T + τ U, where T denotes the duration required to ensure energy transfer to the user who is scheduled to transmit in the first time slot. We assume that the energy harvested by a user from the information transmission of other users is negligible. Downlink and uplink composite fading channels are considered as gamma random variables. The WPCN configurations considered are described below. 1 All PBs are placed around the BS at a fixed distance and at equally spaced angular intervals.

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7.3.1.1

251

Harvesting Energy from a Full-Duplex BS In this configuration, all users replenish their energy solely from the dedicated BS. This is considered as a baseline scenario in which there are no additional sources available for energy harvesting. The full-duplex operation at a BS is defined as follows. •

•

In-band full-duplex (IBFD). In this case, the BS broadcasts energy to users and receives information from the users in the same channel at the same time. Therefore, SI becomes a critical issue. Out-of-band full-duplex (OBFD). In this case, the energy transfer and information reception occur in different channels at the same time. Therefore, there is no SI.

Users who are scheduled to transmit at a later time can accumulate more energy from the BS (i.e., during the uplink transmission of users scheduled earlier). IBFD operation is achieved with a shared antenna at the BS that separates the transmitting and receiving circuit chains through a circulator [6]. On the other hand, OBFD operation is achieved using a traditional antenna with pass-band filters. The energy harvested by an arbitrary user scheduled in time slot u can thus be given as follows: Eu = ηPtot (T + τ (u − 1))r−β ζ0 ,

(7.1)

where Ptot is the maximum transmit power of the IBFD/OBFD BS with which it transmits throughout the duration Tframe , r is the distance of the user from the BS, β is the path-loss exponent, η is fixed and represents the receiver harvesting efficiency, and ζ0 denotes the downlink composite fading channel gain. Note that η can vary depending on the harvested energy levels, in practice. Since each user can harvest energy until its transmission time slot, the total time for the energy transfer of a user scheduled in time slot u is given by T + τ (u − 1). Given the energy harvested by a user who is scheduled to transmit in slot u, its transmit power is given as Pu =

ξ Eu Ptot (T + τ (u − 1))ηξ r−β ζ0 = . τ τ

(7.2)

Since the users are uniformly distributed within the cellular region, the distribution of the distance of a given arbitrarily located user from the BS can be given as follows [7]: fr (r) =

2r . R2

(7.3)

On the other hand, the distance distribution of a user who is located at the maximum distance from the BS can also be given by using the tools from ordered statistics as follows [7]: fr(U) (r) = U(Fr (r))U−1 fr (r).

(7.4)

The energy harvested by the farthest user scheduled in time slot u can thus be defined by replacing r in (7.1) with r(U) = max{r1 , r2 , . . . , rU }. Note that the users are selected 10 Mar 2017 at 08:08:00, .008

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arbitrarily to transmit in each time slot. Therefore, a specific user (either an arbitrarily located one or the farthest user) has an equal probability of transmission in each time slot.

7.3.1.2

Harvesting Energy from PBs In this configuration, users harvest energy from PBs that are symmetrically deployed at a distance ρ from the BS in a circular fashion. All users continue to harvest energy from PBs until their transmission time slot begins. The PBs are dedicated energy sources that can deliver energy in both isotropic and directed modes [8]. Isotropic mode. In the isotropic mode, a PB radiates power in an omni-directional manner to provide energy to all users at the same time. Hence, a user can harvest energy from all PBs; therefore, the harvested energy of a user scheduled to transmit in time slot u can be given as follows: E¯ u = PPB η(T + τ (u − 1))

M 

di−α ζi ,

(7.5)

i=1

where di is the distance between a given user and the ith PB, the transmit power of a PB is considered as PPB = Ptot /M to ensure that the total power consumption is the same as is the case in full-duplex configuration, ζi denotes the composite fading channel gain between a given user and the ith PB, and α denotes the path-loss exponent of the energy transfer links from PBs. We consider that the energy transfer links from PBs use a separate frequency band. Thus the path-loss exponent α need not be the same as β. Directed mode. In the directed energy transfer mode, a given user makes a request and harvests energy only from the nearest PB. For analytical tractability, we model the harvested energy of a given user, using the beamforming response of the main lobe of its nearest PB [8]. Since, with efficient beamforming, the power from the side-lobes of the other users’ directed beams cannot contribute much to the harvested energy levels of a given user, we consider the beamforming response only from the main lobe (w), which is fixed. The energy harvested by a user in the directed mode can thus be given as follows: ηPtot −β (7.6) (T + τ (u − 1))wd(1) ζ , E˘ u = U where the transmit power of a PB Ptot /M is further divided by the average number of users U/M associated with it.2 This ensures a finite power for each user associated with a PB and thus allows continued energy transfer for each user until its transmission time an arbitrary user and its nearest PB. Owing slot begins. Also, d(1) is the distance between *

to the symmetric deployment of PBs, d(1) = ρ 2 + r2 − 2rρ cos(θ − θ(1) ), where θ(1) denotes the angle between the reference x-axis and the line connecting the BS and the nearest PB to a given user. Note that θ(1) −π/M ≤ θ ≤ θ(1) +π/M (see Figure 2 in [5]).

2 For analytical tractability, we approximate the number of users associated with a PB by its average, i.e.,

U/M; however, in the simulations, we divide Ptot /M by the actual number of users available within the sector of each PB.

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253

Consequently, Pu can be calculated as Pu = ξ E¯ u /τ and Pu = ξ E˘ u /τ for the isotropic and directed modes, respectively.

7.3.2

Performance Metrics Given the energy available at an arbitrarily selected user scheduled to transmit in time slot u, its SNR outage probability can be defined as follows:   Pu x−β χ Ou = Pr(γu < γth ) = Pr < γth , (7.7) N0 where x = r for the first two configurations and x = d(1) for the third configuration, γu denotes the SNR of an arbitrarily selected user scheduled to transmit in time slot u, γth is the minimum required SNR level to achieve a target rate Rt , χ denotes the uplink composite shadowing and fading channel, and N0 represents the thermal noise power. To incorporate the impact of considering two frequency resources in out-ofband approaches (i.e., OBFD, configuration 2), we define γth = 2yRt −1 , i.e., y = 2 for the OBFD cases and y = 1 for the IBFD case. Also, in the IBFD case, the SI power, which is commonly modeled by Ptot /K [4], is added to the noise power, where K is the SI cancellation value. The total SNR outage probability of any user can then be given  as O = U u=1 Ou /U. Along the same lines, the spectral efficiency of transmission by an arbitrarily selected user scheduled to transmit in time slot u can be defined mathematically as follows: Cu =

τ (1 − Ou ) log2 (1 + γu ). yTframe

(7.8)

 The total spectral efficiency of a user can then be given as C = U u=1 Cu /U. Similarly, the SNR outage probability and spectral efficiency for a user located farthest from the BS can be defined by replacing r with r(U) in (7.7) and (7.8), respectively.

7.3.3

SNR Outage Analysis: Configuration 1 Given the definition of SNR outage in (7.7), the cumulative distribution function (CDF) of Z can be derived as follows: & ' z κχ ˜ |κχ , 1 + κχ , 1 + κχ − κζ0 FZ (z) = ax 1 F2 χ ζ0 & ' z − bxκζ0 1 F˜ 2 |κζ0 , 1 + κζ0 , 1 + κζ0 − κχ , (7.9) χ ζ0   κχ and b = π cossc(π(κ − κ ))/ ζ0 − κχ ))/ (κζ0 )( χ ζ0 ) ζ0 χ  where a = π cosec(π(κ (κχ )( χ ζ0 )κζ0 . The SNR outage probability of an arbitrarily selected user scheduled to transmit in time slot u can be derived by averaging over r as follows: 6 R 2 Fγu |r (γth )r dr. (7.10) Ou = 2 R 0 10 Mar 2017 at 08:08:00, .008

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7.3.3.1

SNR Outage Probability with Path Loss and Rayleigh Fading If both the uplink and downlink channel experience path loss along with Rayleigh fading (i.e., there is no shadowing), we can simplify Fγu |r (γ ) as follows: 

   γ r2β γ r2β Fγu |r (γ ) = 1 − 2 K1 2 . Ku χ ζ0 Ku χ ζ0

(7.11)

Consequently, the SNR outage probability can be evaluated using (7.10). In addition, a closed-form expression for the SNR outage probability can be derived for the free-space path-loss scenario, i.e., β = 2, as (  Ku χ ζ0 2,1 R4 γth G Ou = 1 − √ 1,3 Ku χ ζ0 2 γth R2

7.3.3.2

   

) 1 1 3 2, 2, 0

.

(7.12)

Approximate SNR Outage: High-SNR Regime Because of the low values of the thermal noise power N0 , the values of γu turn out to be typically high; therefore, using the high-SNR approximation and the fact that l (z, a/b) = (a/b)z /z as a → ∞, we can approximate the SNR outage probability in the high-SNR regime as follows: κ  R2β γth / χ ζ0 Ku ζ0 (κχ − κζ0 ) , Ou ≈ (κχ )(κζ0 + 1)(βκζ0 + 1) 

κζ 0 < κ χ .

(7.13)

As a by-product of the approximate approach, we will show that the distance Rth beyond which a user scheduled to transmit in time slot u experiences a 100% SNR outage can be calculated by ensuring that Ou = 1. This can be done in an exact way by 2β substituting Fγu (γth ) = FZ (γth Rth / (Ku χ )) and then finding the root of Ou numerically. The root can be calculated by using any standard mathematical software package such as MAPLE or MATHEMATICA. Note that the support set of a Gamma random variable (RV) is in the range (0, ∞). Thus, even for very large distances, the exact Ou cannot be one. For evaluation purposes, if Ou approaches 0.999, we consider it as unity. On the other hand, in the approximate asymptotic approach using (7.13), the calculation of Rth simplifies to finding the root of the following: 6 Ou ≈

 ∞

2β

γth Rth /( ζ0 Ku χ )

0

κζ

κζ0 (κζ0 )

0

fχ (χ )dχ = 1.

(7.14)

Rth can then be characterized by using (7.14) in a closed form as follows:  Rth =

(Ku χ ζ0 )κζ0 (κχ )(κζ0 + 1) κζ γth 0 (κχ

− κζ0 )



1 2βκζ

0

,

κχ > κζ0 .

Similarly, for κχ < κζ0 , we can derive Rth in a straightforward manner. 10 Mar 2017 at 08:08:00, .008

(7.15)

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7.3.3.3

255

Analysis of Spectral Efficiency The spectral efficiency of transmission by a user scheduled to transmit in time slot u can be given using (7.8) as Cu =

7.3.4 7.3.4.1

2τ (1 − Ou ) yTframe R2 Ku χ ζ0 (κχ )(κζ0 ) ) ( 6 ∞6 R γ r2β 2,0 × log2 (1 + γ )G0,2 |κχ − 1, κζ0 − 1 r2β+1 dr dγ . (7.16) Ku χ ζ0 0 0

Harvesting Energy from PBs: Configuration 2 Isotropic Mode In this mode, all PBs transmit in an omni-directional manner; thus a given user can harvest energy from all PBs simultaneously. In this configuration, to derive the SNR outage probability of an arbitrarily located user we need to derive the statistics of γu , which is the sum of M RVs. Since deriving the probability distribution function (PDF) of the sum of RVs requires convolution, this reduces the tractability of the analytical framework. For this reason, we resort to a moment generating function (MGF)-based approach to derive both the SNR outage probability and the spectral efficiency of the user. Our approach proceeds as follows: first we derive the MGF and characteristic function (CF) of Z. Conditioned on the location of the user as (r, θ ), we then derive the conditional MGF and CF of γu by exploiting the scaling property of the MGF. Finally, we average over r and θ to determine the total SNR outage probability and spectral efficiency. This averaging would be different for an arbitrarily located user and the user farthest from the BS. Combining the definition of Pu in (7.5) and that of γu in (7.7), we can write γu =

M  i=1

γu,i =

M  Ku d−α r−β Zi i

i=1

M

,

(7.17)

where γu,i denotes the SNR of the scheduled user when it harvests energy  ∞ from the ith PB. Applying the definition of an MGF, i.e., MZi (t) = E[e−tZi ] = 0 e−tz fZi (z)dz, a closed-form MGF of Zi can be derived as follows [9, equation (7.813/1)]:  & '  1 1 0  MZi (t) = G2,1 . (7.18) t χ ζ0 (κχ )(κζ0 ) 1,2 t χ ζ0  κχ − 1, κζ0 − 1 Now, by conditioning on the location of a given user as (r, θ ) from the BS and exploiting the scaling property of the MGF, i.e., MaZi (t) = MZi (at), we can derive the conditional MGF of γu,i . Note that the RVs γu,i , ∀i = 1, 2, . . . , M, are correlated because of the users’ locations. Thus, for analytical tractability and to avoid the complexity of dealing with M correlated random variables, we discretize the cellular region into Y circular zones of equal width and W equal angular intervals (other discretization approaches can also be used here, as mentioned in [10]). Conditioning on the location of a user at the circular ring of radius ry and angle θw , its distance from a given PB i can be calculated 10 Mar 2017 at 08:08:00, .008

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* by using the cosine law as ry2 + ρ 2 − 2ry ρ cos(θw − θi ) in a deterministic way. Note that θi is the angle between the reference x-axis of the BS and the line connecting the BS and PB i (see Figure 2 in [5] for a graphical illustration). For a given value of ry and θw , γu,i ∀i become independent RVs (approximately). The MGF of γu can then be derived as follows:   M −β

Ku ry t M Zi . (7.19) Mγu |ry ,θw (t) ≈ M(ry2 + ρ 2 − 2ry ρ cos(θw − θi ))α/2 i=1

The unconditional MGF of γu can then be derived by averaging over all possible values of ry and θw as Mγu (t) =

Y  W 

Mγu |ry ,θw (t)Pr(r = ry , θ = θw ).

(7.20)

y=1 w=1

Since r and θ are independent random variables, Pr(r = ry , θ = θw ) = Pr(r = ry )Pr(θ = θw ). Note that θ is uniformly distributed between 0 and 2π; therefore, Pr(θ = θw ) = 1/W. On the other hand, the probability that a user is at a distance ry can be given by using the CDF of r as follows: Pr(r = ry ) = Fr (ry ) − Fr (ry−1 ) =

2 ry2 − ry−1

R2

.

(7.21)

The user located between ry and ry−1 is considered to be located at ry . Given the MGF of γu , its CF can be determined as φγu (jω) = Mγu (jω). Using the Gil–Pelaez theorem [11], the probability of an arbitrary RV falling below a given threshold can be evaluated. The SNR outage probability of a user can then be derived using the Gil–Pelaez theorem as follows:   6 1 1 ∞ Im φγu (jω)ejωγth Ou =Pr(γu − γth ≤ 0) = + dω. (7.22) 2 π 0 ω The first step is the application of the lemma, whereas the second step utilizes the fact that γth is a constant and its PDF is a Dirac delta function. Similarly, the spectral efficiency can be given by using the lemma proposed in [12] as 6 ∞ 1 − Mγu (t) −t 1 (7.23) E[ln(1 + γu )] = e dt. Cu = ln(2) ln(2)t 0 The integral can be evaluated by using standard mathematical software packages such as MATHEMATICA.

7.3.4.2

Directed Mode To set the coverage boundaries of each PB, we divide the cellular region into M sectors (see Figure 2 in [5]). Since on average all sectors are identical, the analysis can be conducted for a given user located in the highlighted sector. Without loss of generality, this analysis can be applied to any other user located in any other sector. In this section, we derive the SNR outage probability and spectral efficiency for a user scheduled to 10 Mar 2017 at 08:08:00, .008

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transmit in time slot u considering a directed energy transfer from the nearest PB. Using the expressions derived, we optimize the distance of the PBs such that the SNR outage probability is minimized. Given the definition of E˘ u from (7.6), and Pu and γu in (7.7), γu can be expressed as −α −β r Z/U. Conditioned on r and θ, using (7.9), we can derive the outage γu = Ku wd(1) probability of a given user scheduled to transmit in time slot u as   6 R 6 π/M α Uγth rβ d(1) FZ (7.24) fr (r)fθ (θ )dr dθ. Ou = Ku w r=0 θ=−π/M The above expression can be solved numerically by using MATHEMATICA and MAPLE. However, to avoid the computation of double integrals, we further simplify the expressions for the SNR outage probability by exploiting the high-SNR assumption and obtain some approximate results as discussed in the following. Using a high-SNR approximation and the fact that l (z, a/b) = (a/b)z /z as a → ∞, we can approximate the SNR outage probability in the high-SNR regime considering κζ < κχ as follows:  κ M(κχ − κζ ) Uγth /( ζ χ Ku w) ζ Ou ≈ π R2 (1 + κζ )(κχ ) 6 R 6 π/M r1+βκζ (r2 + ρ 2 − 2rρ cos(θ − θ(1) ))ακζ /2 dr dθ , (7.25) × 0

−π/M

where fθ (θ ) = M/(2π ). The SNR outage expression above can be simplified for certain special cases. Using the simplified expressions, the optimal ρ is then derived as illustrated in the following corollaries. 1.

Closed-form SNR outage probability for ακζ = 2. Consider a case in which the product of the path-loss exponent α and the shape factor of the composite fading downlink channel κζ becomes equal to 2. Then the SNR outage probability in (7.25) can be derived in closed-form as follows:  κ (κχ − κζ ) Uγth /( ζ χ Ku w) ζ Ou ≈ (1 + κζ )(κχ )    2Rβκζ +2 2Rβκζ ρ 2 4Rβκζ +1 ρM π × + − sin . (7.26) 4 + βκζ 2 + βκζ (3 + βκζ )π M Note that the case ακζ = 2 reflects the channel conditions of practical relevance. For instance, κζ = 1 and α = 2 represent a Rayleigh fading channel with freespace path loss. Also, κζ = 1/2 and α = 4 represent a severe fading channel with higher path loss. When β = α, (7.26) can be further simplified as   (κχ − κζ ) R4 /3 + R2 ρ 2 /2 − 4ρR3 M/(5π )sin(π/M) Ou ≈ . (7.27)  −κ Uγth /( ζ χ Ku w) ζ (1 + κζ )(κχ ) The optimal distance of the PBs can then be obtained by using the expression in (7.26) as stated in the following corollary. 10 Mar 2017 at 08:08:00, .008

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2.

Optimal distance of PBs for ακζ = 2. By differentiating the expression in (7.27) with respect to ρ and equating it to zero, i.e.,   4Rβκζ +1 M 4Rβκζ ρ π ∂Ou − = sin = 0, (7.28) ∂ρ 2 + βκζ (3 + βκζ )π M we can derive a closed-form expression for the optimal distance of PBs as follows: (2 + βκζ )MR sin(π/M) ρ∗ = . (7.29) (3 + βκζ )π

−α −β Note that γu = wKu d(1) r Z/U. Conditioned on r and θ, we can write fγu |r,θ =    α α /(wK ) . The spectral efficiency of a given user schedβ β Ur d(1) /(wKu ) fZ Uγu r d(1) u uled to transmit in time slot u can then be derived as follows: 6 R 6 π/M Ulog2 (1 + γu ) Cu = −β d −α 0 −π/M wKu r (1)   β α − fZ Uγu r d(1) /(wKu ) fr (r)fθ (θ )dr dθ. (7.30)



The above expression can be solved numerically by using any standard mathematical software package. Note that the performance analysis of the farthest user can be done in a straightforward manner by applying the distribution of fr (r) as given in (7.4) to the aforementioned derivations. The step-by-step details of the theoretical results presented in this section are available in [5].

7.4

Numerical Results and Discussion In this section, we demonstrate the usefulness of the framework in quantifying and optimizing the network performance metrics, such as the SNR outage probability and spectral efficiency, as functions of network design parameters. The expressions are validated by Monte Carlo simulations. A comparative performance analysis of the network configurations is also conducted. The radius of the macrocell is taken as 600 m and the path-loss exponents β and α are taken as 2. The generalized-K composite fading channel for the downlink is approximated by the gamma distribution, i.e., fζ (ζ ) is approximated as (2, 2). The composite fading channel for uplink transmission fχ (χ ) is approximated as (1, 1). The antenna array gain is taken as w = 25, the maximum transmit power of the BS for energy transfer is Ptot = 20 W, and thermal noise power is σ 2 = 10−12 W/Hz. The number of users is set as U = 20 and the transmission time slot for each user is τ = 1 ms. The target rate is taken as Rt = 1.73 bps/Hz, a user’s receiver harvesting efficiency as η = 0.6, and the SI cancellation capability as K = 130 dB. Without loss of generality, ξ = 1. The values of all of the abovementioned parameters remain the same unless stated otherwise. 10 Mar 2017 at 08:08:00, .008

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100

SNR Outage Probability

IBFD OBFD

10−1

10−2

10−3

80

100

120

140

160

180

200

Self−Interference Cancellation Value (K) [dB]

Figure 7.2 SNR outage probability of an arbitrarily located user with IBFD/OBFD BS as a

function of the SI cancellation value.

7.4.1

IBFD versus OBFD Figure 7.2 depicts the SNR outage probability of an arbitrarily located user with IBFD and OBFD BS as a function of the SI cancellation value K. It can be observed that the higher the value of K, the lower the SNR outage probability with IBFD BS. To achieve the required rate of Rt , γth = 10 for OBFD BS and γth = 2.73 for IBFD BS. Although IBFD requires a lower SNR target, it outperforms OBFD only with very high SI cancellation. Hence, use of the OBFD mode is more favorable and less costly at high-power BSs. Figure 7.3(a) depicts the SNR outage probability of an arbitrarily located user as well as that of the user farthest from the BS both for half-duplex and for OBFD configurations. As expected, the SNR outage probability of the farthest user provides a lower bound on the average performance of an arbitrarily located user. The results based on the closed-form exact expressions perfectly match with the Monte Carlo simulation results. On the other hand, the simplified expressions obtained using the high-SNR approximation are also reasonably accurate for medium to high values of T/τ . It is observed that higher values of T/τ tend to reduce the SNR outage probability of both an arbitrarily located user and the farthest user. For very high values of T/τ (i.e., T τ ), it can be seen from Figures 7.3(a) and (b) that the performances of half-duplex, IBFD, and OBFD configurations converge to the same value. This is due to the fact that very high levels of T allow higher harvested energy levels; thus the energy harvested during time T dominates over the energy harvested during transmission time slots of duration τ . This is why the differences in the performance gains for all configurations become negligible. 10 Mar 2017 at 08:08:00, .008

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Half−Duplex BS

SNR Outage Probability

100 SNR Outage Probability

100

High SNR Approximation Simulations Arbitrary User; Analysis Farthest User; Analysis

−1

10

10−2 Out−of−Band Full−Duplex BS 10−3

−4

10

−2

−1

0

1

2

10 10 10 10 10 Ratio of Initial Energy Harvesting Time and Transmission Time (T/t)

Half−Duplex BS OBFD BS IBFD BS

10−1

10−2

10−3

10−4 100 102 10−2 10−1 101 Ratio of Initial Energy Harvesting Time and Transmission Time (T/t)

Figure 7.3 (a) Outage probability of an arbitrarily located user and of the farthest user as a

function of the ratio of harvesting to transmission time considering both half-duplex and OBFD configurations. (b) Outage probability of an arbitrarily located user considering half-duplex, IBFD, and OBFD BS configurations; K = 130 dB.

7.4.2

Harvesting from PB(s): impact of ρ Figure 7.4(a) depicts the SNR outage probability of an arbitrarily located user in configuration 2, i.e., when a user is allowed to harvest energy from M PBs until its scheduled time slot arrives. The PBs are considered to be deployed either randomly or in a symmetric manner. Once energy has been harvested, information is transferred to the conventional half-duplex BS. The SNR outage probability tends to reduce significantly for both M = 2 and M = 10 compared with the OBFD BS. On the other hand, configuration 2 outperforms IBFD BS for a large number of PBs, i.e., for M = 10. This result suggests the usefulness of configuration 2 rather than an IBFD/OBFD BS for a reasonable value of M. Note that using an IBFD BS always requires cancellation of strong SI within each time frame Tframe . On the other hand, configuration 2 requires a one-time deployment of low-cost PBs without any requirement for backhauling. It is also observed that the optimal placement of the PBs in a symmetric deployment significantly outperforms random deployment. Especially for a small number of PBs, the gains are observed to be significant over a wide range of ρ, which would be more desirable for an operator. Figure 7.4(b) illustrates the directed mode of PBs in configuration 2, i.e., when a given user is allowed to harvest energy from its nearest PB in a directed manner until its transmission time slot arrives. The analytical results corroborate the Monte Carlo simulation results. The main observations for the random and symmetric deployment remain the same. It can be observed that an increase in the number of PBs impacts their optimal placement, i.e., shifts their locations away from the BS while reducing the SNR outage probability significantly. The directed mode tends to outperform the isotropic mode significantly, especially for high values of M. It can be noticed that the optimal distance of PBs, for a given M, remains the same for both isotropic and directed modes of configuration 2. The reason is that, when a user harvests energy from the nearest PB (in directed mode), which is placed optimally, the additional energy harvested from the remaining PBs (in isotropic mode) simply adds to that value. 10 Mar 2017 at 08:08:00, .008

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Figure 7.4 SNR outage probability of an arbitrarily selected user as a function of ρ when energy

is harvested from PB(s) and information is transferred to the conventional half-duplex BS considering both (a) the isotropic mode and (b) the directed mode of energy transfer from PBs. Both random and symmetric deployments of PBs are considered.

7.4.3

Harvesting from PB(s): impact of M Figure 7.5 depicts the SNR outage of an arbitrarily located user in configuration 2 as a function of the number of PBs M considering the optimal placement of PBs for each value of M as derived in corollary 1. First, it can be observed that an increase in M tends to reduce the SNR outage probability in the isotropic mode. Although the power per PB decreases with increasing M, the option of harvesting from all PBs continues to reduce the SNR outage probability. However, this reduction becomes marginal when M increases from 15 to 30. Second, symmetric deployment continues to outperform random deployment for any number of PBs. Third, the gain of the directed mode of operation with the symmetric deployment of PBs exceeds those of all other configurations.

7.5

Summary We have investigated and comparatively analyzed the usefulness of several different deployments of dedicated energy transmitters as well as information receivers. Numerical results have demonstrated the significance of the limited and planned 10 Mar 2017 at 08:08:00, .008

Hina Tabassum and Ekram Hossain

Table 7.1. Qualitative comparison of the WPCN configurations considered Feature

Harvesting from full-duplex BS (configuration 1)

Harvesting from PBs (configuration 2)

Complexity Operating cost Implementation cost Performance Interference

High Strong self-interference cancellation Additional RF antenna or circulators

Low Additional channel Deployment of PBs

Low Strong self-interference

High No intra-cell interference

10–2

Isotropic SNR Outage Probability

262

Directed

10–3 Out-of-Band Full-Duplex BS Analysis High SNR Approximation Random Deployment; Sim Symmetric Deployment; Sim In-Band Full-Duplex BS

5

10

15

20

25

30

Number of Power Beacons (PBs) Figure 7.5 SNR outage probability of an arbitrarily selected user as a function of M when energy

is harvested from PB(s) and information is transferred to the conventional half-duplex BS considering both (a) the isotropic mode and (b) the directed mode of energy transfer from PBs. Both random and symmetric deployments of PBs are considered.

deployment of the dedicated energy transmitters as well as information receivers (e.g., PB-assisted distributed antenna element setup) compared with unplanned deployment. Closed-form expressions have been derived for the SNR outage probability in scenarios of practical relevance. Table 7.1 provides a qualitative overview of the three configurations considered, in terms of BS complexity, implementation costs, performance, and the intra-cell interference conditions. In most cases, the deployment of PBs for energy transfer is observed to be beneficial compared to having a centralized BS that takes care of both energy transfer and information reception while operating in half-duplex, IBFD, or OBFD mode. The IBFD BS outperforms the OBFD BS, given a very high SI cancellation capability. Also, in this case, the IBFD BS outperforms configuration 2 if the number of 10 Mar 2017 at 08:08:00, .008

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PBs is smaller and/or the PBs are not placed optimally. The cost of SI cancellation in each time frame can be significant for high-powered BSs and is a running cost that is incurred every time frame. Conventional duplexers cannot be used to separate transmit and receive RF chains due to the in-band operation. A new circuit such as a circulator may be required at the BS to enable full-duplex operation [2]. Configuration 2 incurs a one-time deployment cost of PBs, which is less expensive because there are no backhaul requirements. Thus, we propose configuration 2 with limited and optimal deployments of PBs to improve performance for users in terms of their SNR outage probability and spectral efficiency. This could reduce the burden of energy transfer to far-away users from a centralized BS in an efficient manner. For a low density of users, directed energy transfer (with sufficient antenna gains) from the nearest PB is the most suitable mode of operation. However, when the number of users is very large (i.e., any two users can be close to each other with a very high probability), the probability of a given user receiving energy from multiple directed beams (i.e., beams that are intended to serve other users in the vicinity of that given user) becomes high. In such a case, the framework developed here, where we consider the energy only from the intended lobe of a user, provides a lower bound on the total amount of harvested energy and in turn the upper bound on the SNR outage probability. In extremely dense situations, the directed beamforming to many users is approximately omni-directional. Thus isotropic transmission then becomes a more favorable option. Compared with a large number of randomly placed PBs, a small number of geographically planned PBs will suffice for achieving performance gains while minimizing the deployment costs. The analytical framework can be extended in several directions, for example, to consider multi-cell systems and to capture the interplay of inter-cell interference or inter-cell energy transfer on the performance of transmission by users, and to consider minimum-energy outage events, i.e., when a device cannot transmit below a threshold.

References [1] E. Hossain, M. Rasti, H. Tabassum, and A. Abdelnasser, “Evolution toward 5G multitier cellular wireless networks: An interference management perspective,” IEEE Wireless Communications, vol. 21, no. 3, pp. 118–127, June 2014. [2] K. M. Thilina, H. Tabassum, E. Hossain, and D. I. Kim, “Medium access control design for full duplex wireless systems: Challenges and approaches,” IEEE Communications Magazine, vol. 53, no. 5, pp. 112–120, May 2015. [3] H. Ju and R. Zhang, “Throughput maximization for wireless powered communication networks,” IEEE Transactions on Wireless Communications, vol. 13, no. 1, pp. 418–428, January 2014. [4] H. Ju and R. Zhang, “Optimal resource allocation in full-duplex wireless-powered communication network,” IEEE Transactions on Communications, vol. 62, no. 10, pp. 3528–3540, September 2014. [5] H. Tabassum and E. Hossain, “On the deployment of energy sources in wireless-powered cellular networks,” IEEE Transactions on Communications, vol. 63, no. 9, pp. 3391–3404, July 2015. 10 Mar 2017 at 08:08:00, .008

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[6] G.-P. Liu, R. Yu, H. Ji, V. Leung, and X. Li, “In-band full-duplex relaying: A survey, research issues and challenges,” IEEE Communications Surveys and Tutorials, vol. 17, no. 2, pp. 500–524, January 2015. [7] H. Tabassum, E. Hossain, M. Hossain, and D. Kim, “On the spectral efficiency of multiuser scheduling in RF-powered uplink cellular networks,” IEEE Transactions on Wireless Communications, vol. 14, no. 7, pp. 3586–3600, July 2015. [8] K. Huang and V. K. Lau, “Enabling wireless power transfer in cellular networks: Architecture, modeling and deployment,” IEEE Transactions on Wireless Communications, vol. 13, no. 2, pp. 902–912, February 2014. [9] S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th edn., New York: Academic Press, 2000. [10] H. Tabassum, F. Yilmaz, Z. Dawy, and M.-S. Alouini, “A statistical model of uplink intercell interference with slow and fast power control mechanisms,” IEEE Transactions on Communications, vol. 12, no. 1, pp. 206–217, September 2013. [11] Q. T. Zhang, “Outage probability of cellular mobile radio in the presence of multiple Nakagami interferers with arbitrary fading parameters,” IEEE Transactions on Vehicular Technology, vol. 44, no. 3, pp. 364–372, May 1996. [12] K. A. Hamdi,“A useful lemma for capacity analysis of fading interference channels,” IEEE Transactions on Communications, vol. 58, no. 2, pp. 411–416, February 2010.

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8

Ambient Wireless Energy Harvesting in Small Cell Networks: Performance Modeling and Analysis Ahmed Hamdi Sakr, Hina Tabassum, and Ekram Hossain

8.1

Introduction Small cell networks (SCNs) are envisioned as a key enabling feature of next-generation wireless networks that can meet the high capacity requirements in outdoor/indoor environments [1]. The successful implementation of SCNs faces several challenges. For instance, the increase in co-channel interference (CCI) due to densification of small cells can significantly degrade the achievable network capacity. Moreover, the subsequent increased energy consumption of the system is undesirable from both environmental and economical perspectives. Finally, providing grid power to all small cell base stations (SBSs) may not always be feasible due to their possible outdoor/remote/hard-to-reach locations. Thanks to the recent advancements in wireless energy harvesting (EH) techniques, it has become feasible to power small devices wirelessly. Wireless EH thus enables dense deployment of SBSs irrespective of the availability of power grid connections. It is important to note that dedicated EH leverages the deployment of dedicated energy sources. Therefore, additional resource/power consumption is unavoidable [2]. Consequently, ambient EH is crucial to reduce the grid power consumption of cellular networks. Unfortunately, owing to the dependence of energy harvested from renewable energy sources on temporal/geographical/environmental circumstances, consistent performance at the base stations (BSs) may not be guaranteed. Also, harvesting energy from renewable energy sources may require an extra hardware setup of solar panels and/or wind turbines. Thus, the significance of investigating other kinds of ambient sources in order to minimize the grid power consumption of cellular networks becomes evident. Motivated by the aforementioned facts, in this chapter, we focus on RF-based ambient EH small cell networks and highlight the corresponding challenges from implementation and operation perspectives. These challenges arise due to factors such as nondeterministic energy arrival patterns, EH mode selection, energy-aware cooperation Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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among base stations, etc. Next, we provide a brief overview of the existing literature in the context of the challenges discussed. The review provided highlights the research gaps and points out future research directions. Finally, we investigate the performance of a K-tier uplink cellular network where cellular users harvest RF energy from the concurrent downlink transmissions from all network tiers. Then, each user stores the harvested energy in an attached battery until the amount of energy stored therein is sufficient to perform channel inversion power control. We use tools from stochastic geometry and Markov chain theory to model the randomness and battery evolution of the SBSs. Numerical results are presented to validate the accuracy of the analysis.

8.2

Challenges in Ambient Wireless Energy Harvesting in Small Cell Networks Ambient EH from renewable energy sources is very promising. However, the amount of energy harvested remains limited by the geographical, seasonal, and environmental situation. Recently, there has been a shift toward considering RF-based ambient EH in order to accumulate energy reliably in a variety of environmental settings. Nevertheless, RF-based ambient EH has its own limitations that need be tackled before implementing such a system in practice. In this context, some of the main challenges are discussed in the following [3].

8.2.1

Uncertain Energy Arrival Rate The degree of uncertainty in RF-based ambient EH at SBSs is quite low compared with that in EH from renewable energy sources. The reason is that the locations and traffic patterns of the SBSs deployed in a given area remain relatively fixed over time. Nonetheless, reliable energy transfer may not always be guaranteed, owing to the adaptive transmission policies of the SBSs as well as temporal and spatial variations of wireless channels. To analyze the performance of such systems, it is essential to precisely model the energy arrival rate at EH devices. Also, in such a system, a 100% deployment of off-grid SBSs may not be feasible due to insufficient energy being harvested from the less-dense fixed power TV/radio broadcast towers, macro BSs, and the reduced power transmissions of the other off-grid SBSs. Thus, to maintain a balance between grid energy consumption and the achievable communication performance, the SCNs should use a mixture of on-grid and off-grid SBSs.

8.2.2

Modeling Co-channel Transmissions Co-channel RF transmissions limit the performance of conventional cellular networks and their impact will be more significant in densely deployed SCNs. However, strong co-channel transmissions can be useful to harvest energy in EH-enabled SCNs. In the downlink, the tradeoff between the amount of energy harvested at an off-grid SBS and the amount of interference incurred by a given user needs to be optimized. This can

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be done by optimizing the intensity of active SBSs or the proportion of on-grid and off-grid SBSs such that the network throughput, grid power consumption, and, in turn, energy efficiency can be improved. Note that the harvested energy and the CCI are crucial quantities for performance analysis of ambient RF-based EH SCNs. Thus, it is important to develop analytical models to characterize the co-channel transmissions of SBSs in various network deployment scenarios.

8.2.3

Energy Cooperation/Coalition among SBSs Traditionally, cooperation among multiple BSs is carried out to enhance the diversity of transmitted signals and to perform interference mitigation. However, in EH-enabled ultra-dense SCNs, cooperation may also be required in order to overcome the energy imbalance among various on-grid/off-grid SBSs. This can be done by allowing nearby SBSs to cooperate by sharing their energy states/requirements/transmission policies with each other and by enabling a cognitive decision-making capability at each SBS about the consumption or utilization of its harvested energy. For instance, knowing the transmission pattern of nearby SBSs, an off-grid SBS can estimate the amount of energy it can harvest. Then, with limited information exchange, the off-grid SBS can likely encourage nearby SBSs to continue their transmission if the overall utility of their coalition can be increased.

8.2.4

Enabling On-Grid/Off-Grid/Idle Mode Selection Owing to the uncertainty of the energy arrival rate, each SBS in an RF-based ambient EH network must be connected to the power grid, unless there is a deployment/implementation constraint. This enables an SBS to avoid severe transmission outage due to insufficient harvested energy by operating adaptively in on-grid, off-grid, and idle modes. As discussed before, there could be a central entity that can optimize the proportions of on-grid, off-grid, and idle SBSs in the network and forward the decision to all SBSs. The SBSs would then switch their mode accordingly. However, this method may impose significant signaling/information overhead and cannot be scalable for ultradense deployments. On the other hand, fully distributed mode selection allows an SBS to decide its mode individually in order to enhance its own utility. However, this may degrade the overall system utility. Therefore, semi-distributed mode selection would be more attractive.

8.2.5

Energy-Aware User Offloading Energy cooperation among SBSs allows SBSs to operate in small coalitions such that their overall utilities can be maximized. In this context, energy-aware user offloading can be of significant importance. For example, an SBS may switch to grid power because of its reduced energy level; however, the SBS could possibly coordinate with neighboring SBSs to handle its traffic load and move into idle mode instead. This can improve the overall utility of the coalition by reducing grid-power consumption as well as interference with other SBSs.

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8.3

RF Ambient Energy Harvesting: Literature Review We provide a brief overview of the recent literature in the context of challenges mentioned before. More precisely, we focus on the references that are related to ambient RF EH in different communication networks/scenarios such as cognitive radio, wireless sensor networks, device-to-device (D2D) communication, SCNs, etc. To highlight the existing research gaps, we comparatively analyze work by various authors, considering their problems/assumptions, energy arrival models, and solution methods, and the benefits and limitations of ambient energy transfer in such communication networks. A qualitative summary of the review is provided in Table 8.1 [3].

8.3.1

Modeling of Energy Arrival Rate For guaranteed quality-of-service (QoS), precise modeling of RF energy arrivals (cochannel transmissions) is crucial, which depends on accurate modeling of the transmit power, locations, and density of the interfering BSs in various deployment scenarios. In this context, a variety of energy arrival models have recently been considered in order to analyze the performance of RF-based EH networks.

8.3.1.1

Arbitrary Energy Arrival In [11], ambient EH (modeled using a sequence of arbitrary i.i.d. random variables) has been exploited for mobile ad-hoc networks. Given the energy arrival statistics, the network rate is maximized by optimizing the transmission powers of transmitters. For numerical results, the energy arrival rate is modeled by a chi-squared distribution. Energy harvested from other transmitters is not considered. The authors of [9] consider maximizing the average throughput of the secondary network (SN) by optimizing the spectrum sensing time (i.e., the time taken to detect unused primary spectrum) and sensing threshold of the secondary transmitters (STs). The arrival of energy at the STs is modeled by an i.i.d. random process.

8.3.1.2

Poisson Point Process (PPP)-Based Energy Arrival In [18], the cellular users harvest energy from the downlink transmission of K-tier BSs and use the harvested energy for their uplink data transmission. Since the spatial distribution of BSs is modeled by independent PPPs, the energy arrival rate depends on the parameters of the PPPs. By using tools from stochastic geometry and queuing theory, closed-form expressions are derived for the transmission probability (i.e., the probability that a user’s battery has harvested sufficient energy for transmission), coverage probability (i.e., the probability that the signal-to-interference-plus-noise ratio (SINR) at the receiving BS is higher than the required threshold), and success probability (i.e., the probability that both transmission and coverage probabilities are satisfied) of a typical user. Ambient EH is also investigated in [10] in the context of a cognitive radio network, where STs harvest energy from primary transmitters (PTs). Since PTs and STs are modeled by PPPs, the energy arrival rate depends on the PPP for the PTs. By applying tools from Markov chain theory, the transmission probability of STs and the SINR outage probability of both the primary and the secondary networks have been derived.

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Table 8.1 Overview of existing works on RF ambient energy harvesting

Energy arrival model

Solution techniques

Limitations

Objectives and benefits

Ambient EH in a point-to-point wireless link [4]

Deterministic and stochastic (gamma distribution)

Stochastic optimization

Co-tier interference and effect of path loss are neglected

Ambient RF EH in a point-to-point sensor network [5]

Stochastic

Order statistics

Point-to-point uplink in wireless sensor networks (WSNs) [6] Simultaneous wireless information and power transfer (SWIPT) in WSNs for downlink [7] EH from CCI in a point-to-point wireless link [8] Cognitive radio [9]: Secondary transmitters (STs) harvest energy from primary transmitters (PTs) Cognitive radio [10]: STs harvest energy from PTs MANETs [11]

Depends on spatial distribution of cellular transmitters (e.g., DPP) Depends on spatial distribution of transmitters (DPP)

Ginibre point process

Single-slope path-loss model, with fixed distance between sensor and sink and interfering BS Fixed transmit power for ambient RF source

Ginibre point process

Fixed transmit power for ambient RF source

Challenge 8.2.4 Active ratios of the transmitter and the receiver; derive energy cooperation strategies Challenge 8.2.3 Derive closed-form expression for the distribution function of harvested energy Challenges 8.2.1 and 8.2.2 Derive upper bound of power and transmission outage probabilities Challenge 8.2.1 Derive upper bound for power and transmission outage probability

Arbitrary random variable (exponential distribution)

Optimization (heuristic)

Arbitrary random process (i.i.d.)

Optimization

Depends on the PPP of PTs

Markov chain homogeneous PPP

Arbitrary random process (Chi-squared distribution)

Homogeneous PPP random-walk theory

Arbitrary model of energy arrival, limited to single-user setup CCI of ST is ignored, simple i.i.d. for energy arrival, channel model is not considered Single-slope path-loss model, EH from CCI of STs not mentioned EH from CCI is ignored, single-slope path loss

Challenge 8.2.4 Derive the optimal switching mode Challenge 8.2.1 Maximize the average throughput of SN

Challenges 8.2.1 and 8.2.2 Maximize spatial throughput of SN Challenge 8.2.1 Network throughput is maximized

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8.3.1.3

Ginibre-Determinantal Point Process (DPP)-Based Energy Arrival RF-based ambient EH is investigated in the point-to-point uplink [6] as well as downlink transmissions [7] of wireless sensor networks. The spatial distribution of the cellular transmitters and in turn the RF energy arrival depend on a Ginibre-determinantal point process (DPP). Closed-form expressions for the mean and variance of the energy arrival rate are derived. In addition, upper bounds are derived both for the power outage probability (i.e., the probability that the amount of energy harvested is not sufficient) and for the transmission outage probability (i.e., the probability that the transmission rate of a sensor node is below the desired threshold).

8.3.2

Network Operation/Energy Management Issues In [12], different tiers of BSs are modeled as PPPs with varying EH rate, storage capacity, etc. The energy arrival process is modeled by PPP. Each BS decides individually to operate in either active or inactive mode, depending on its energy arrival rate and the energy level of its battery. When a BS decides to be inactive, it increases the load on the neighboring BSs and consequently affects their performance. The availability of a kth-tier BS (i.e., the duration during which a BS is active) is derived and then the availability region is jointly maximized for a general set of kth-tier BSs. The effect of the availability region on the coverage probability and downlink rate of a typical user is also investigated. In [8], CCI (which is completely known at the receiver and modeled arbitrarily) is considered to power a single-antenna receiver in a point-to-point wireless link. The receiver opportunistically harvests energy or receives information, depending on the channel and interference conditions. The authors derive the optimal switching mode for the receiver considering delay-limited and delay-tolerant information transmission cases. In [13], the authors propose two approaches to harvest energy from cyclic prefix (CP) in OFDM receivers to provide the energy required for signal processing at the receiver. The first approach is an ambient RF-based scheme; it is implemented by modifying the receiver architecture such that the receiver is able to harvest energy from CP. The feasibility of this approach is shown in terms of power consumption at the receiver. The second approach is based on a dedicated EH scheme whereby the transmitter controls the amount of energy on the CP to regulate the amount of energy harvested at the receiver. The authors observe that this approach is feasible and provides a self-sustainable receiver. In [5], the authors investigate EH in a time-varying fading environment for point-to-point transmission between a sensor and its sink, considering a single-slope path-loss model. It is assumed that the sink has grid power supply and the sensor harvests energy from ambient RF resources. A closed-form expression for the distribution of harvested energy is derived. For delay-insensitive traffic, the average packet delay is analyzed, whereas for delay-sensitive traffic, the packet-loss probability is analyzed. The authors of [4] propose an energy cooperation scheme for a point-to-point network when both transmitter and receiver have non-idle circuits, i.e., the hardware power consumption is not negligible. Both of them harvest energy from external sources to support

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their communication and the circuit power consumption. In addition, they are able to exchange some of their harvested energy to enhance the communication performance. This paper analyzes the optimal throughput and outage probability for additive white Gaussian noise (AWGN) and the Rayleigh block fading channel, respectively. In the former case the arrival of energy is deterministic, whereas in the latter it is modeled with a gamma distribution. Simulation results show that energy cooperation between the transmitter and receiver can improve the communication performance. In the context of statistical modeling of multi-tier cellular networks, the authors of [14, 15] present a general framework for the performance evaluation of K-tier downlink cellular networks. In this model, the locations of BSs in each tier are modeled according to independent PPPs such that each network tier differs in transmit power, propagation environment, and spatial density. Using the PPP assumption, closed-form expressions are derived for the outage probability and the ergodic data rate. For uplink networks, the authors of [16] consider a single-tier uplink network with fractional power control. A PPP is used to model the locations of the users where each user is assumed to have exactly one BS in her vicinity. Furthermore, the authors of [17] consider uplink transmissions in multi-tier cellular networks. Using stochastic geometry analysis, a general framework is developed for modeling and performance evaluation of the uplink network with truncated channel inversion power control.

8.4

Ambient Energy Harvesting: Network Performance Modeling and Analysis In this section, we consider a K-tier uplink cellular network where cellular users harvest RF energy from the concurrent downlink transmissions from all network tiers [18]. Then, each user stores the harvested energy in an attached battery until the amount of energy stored is sufficient to perform channel inversion power control. In order to evaluate the performance of this network, we propose a comprehensive framework using a stochastic geometry approach to capture the network’s randomness [19–21]. Furthermore, we use Markov chain modeling to take the battery dynamics into account. The performance of the proposed system is quantified in terms of the signal-to-interference ratio (SIR) coverage probability, transmission probability, and success probability. Note that successful transmission happens only when a user has sufficient energy in her battery and the level of the SIR at the receiver is higher than some predefined threshold. We derive simple and closed-form expressions for the probability density functions (PDFs) and cumulative distribution functions (CDFs) of the transmit power and the harvested energy. Under channel inversion power control, we derive a closed-form expression for the SIR coverage probability for cellular users. We use a discretization technique to approximate the battery level after storing the harvested energy, which enables us to use Markov chain modeling to capture the battery dynamics. Using the steady-state probability analysis, we derive simple expressions for the probability of having sufficient energy stored in the battery for transmission using channel inversion power control (which is referred to as the transmission probability). Then, we obtain the overall probability of successful transmission.

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8.4.1

System Model and Assumptions

8.4.1.1

K-tier Cellular Network Model We consider a system with K independent tiers of BSs that differ in spatial densities, receiver sensitivity, and transmit powers. It is assumed that the BSs belonging to tier k are spatially distributed according to an independent PPP k = {xi : i = 1, 2, . . . } ∈ R2 with spatial density λk (BS/km2 ), where xi denotes the location of the ith BS. In addition, BSs belonging to the same tier k have the same receiver sensitivity ρk (W) and transmit power Pk (W). The users are also modeled by an independent two-dimensional PPP u = {yi : i = 1, 2, . . . } with spatial density λu . For the reliability of uplink transmissions, users use channel inversion power control to adjust their transmission powers such that the average power received by the serving BS is equal to its receiver sensitivity. It is assumed that different users in a cell are served by using orthogonal resources (i.e., different time slots and/or channels) and hence there is no intra-cell interference. In addition, we consider universal frequency reuse in which all BSs use the same channel. We focus on a typical user located at the origin (0, 0). We assume a saturation condition in which users and BSs always have data to transmit.

8.4.1.2

Channel Model Channels are assumed to be symmetric where the power of a signal transmitted by any network node (BS or user) is subject to distance-dependent path loss with a rate of r−α , where α > 2 is the path-loss exponent and r is the propagation distance. In addition, all transmissions experience independent Rayleigh fading and the channel power gains are modeled by independent exponential random variables h with unit mean,1 i.e., h(x, y) ∼ Exp(1).

8.4.1.3

User Association In the uplink, a user is associated with the BS that offers the best average channel gain, i.e., lowest path loss. Further, we assume that all BSs employ an open access policy in which any user can associate with any BS from any tier. That is, each user is assumed to be served in the uplink by the nearest BS. For example, for a user located at y ∈ R2 , let xo denote the serving BS with the best channel gain; hence, xo = arg max {x − y−α },

(8.1)

x∈∪K k=1 k

where  ·  is the Euclidean distance. Figure 8.1 shows a realization of a three-tier network with a macrocell network deployed as tier 1, with femtocell and picocell network tiers as tiers 2 and 3, respectively.

8.4.1.4

Energy Harvesting and Battery Model It is assumed that mobile users rely solely on energy harvested from the ambient RF energy sources to power up their devices for uplink transmissions. In this system model, 1 Note that, because of the assumption of independence, we omit the notation denoting BSs’ and users’

locations for both uplink and downlink whenever possible.

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Figure 8.1 A K-tier cellular network in an area of 3 km × 3 km, where K = 3. A macro-tier (squares) with density 0.5(0.52 π )−1 BS/km2 is overlaid with lower-power and

three-times-denser picocells (circles) and five-times-denser femtocells (diamonds). Solid lines show the coverage area of each BS for the uplink association criterion defined in (8.1).

Figure 8.2 Model for an EH user device consisting of a single antenna, an EH module, an energy

storage unit, and a transmission module.

the RF energy sources are the BSs and the users harvest energy from concurrent downlink transmissions from the BSs. Each user’s device is equipped with an EH module to convert the RF power into useful DC power with RF-to-DC conversion efficiency a ≤ 1. Hence, the total power harvested by a generic user located at (0, 0) ∈ R2 at any time slot is given by PH = a

K  

Pk hx−α .

(8.2)

k=1 x∈k

In addition, each user’s device is assumed to be equipped with a power storage unit (i.e., battery) with storage capacity2 B (W). As shown in Figure 8.2, it is assumed that all users have a single-antenna configuration in which the EH and transmission modules share the same antenna. In other words, users are unable to harvest energy 2 Note that the terms “power” and “energy” can be used interchangeably in the context of time-slotted

transmissions.

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and transmit data in the same time slot. Thus, users adopt a time-slotted “harvest-thentransmit” strategy. In this strategy, a user starts to harvest energy from the downlink transmissions and stores this energy in her battery. Upon having a sufficient amount of energy to perform channel inversion power control, a user transmits to her serving BS. That is, the user checks the battery level at the beginning of each time slot and transmits only when it is sufficient to perform channel inversion; otherwise, it harvests and stores more energy. Note that PH is an implicit function of time, since the fading gains are random and assumed to vary over time. That is, the number of time slots used by each mobile device to harvest energy before data transmission is not the same for each transmission. In general, the number of time slots used for energy harvesting is random and differs from one user to another and from one transmission to another even for the same user. Hence, the total amount of power PS (T) stored in a user equipment’s battery after T time slots  o +T PH , where to is the time slot of the last transmission. can be given by PS (T) = tt=t o Figure 8.3 shows an example of the battery level as a function of time to illustrate the behavior of the user according to the EH model described above. We have three main remarks to make regarding this figure. 1.

2. 3.

The number of time slots required to harvest sufficient energy is random, e.g., it is 5, 10, and only 3 time slots for the first, second, and third transmission, respectively. Owing to the network randomness, the amount of energy harvested is not the same in every time slot even though we are considering the same user. The amount of transmit power required for channel inversion is a function of time as can be seen in slots 6, 17, and 21.

Figure 8.3 The total amount of power stored in a user equipment’s battery versus time. Gray areas

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8.4.2

275

Uplink Transmission Probability We define the transmission probability ηk as the probability of a user associated with tier k having sufficient energy stored in her battery to be able to perform channel inversion toward her serving BS. That is, the energy harvested by this user exceeds the amount of transmit power required in order to have a received power equal to or larger than the BS’s receiver sensitivity. Now we derive the distributions of the harvested power and the transmission power for a typical user. Then, we obtain the transmission probability. •

Analysis of harvested power. First of all, we define the amount of power received  at the typical user from tier k as Pk = a xi ∈k Pk hxi xi −α , where PH = K k=1 Pk . Then, we obtain the Laplace transform of PH so that the PDF can be obtained by taking the inverse Laplace transform. The Laplace transform /K we then have that of PH is given by LPH (s) = k=1 LPk (s). By definition,  ∞ LPk (s) = exp −2π λk 0 (/ (1 + (1/(saPk )) α ))dr . After some mathematical manipulations and substituting uα = (1/(saPk ))rα , we obtain LPH (s) =    2/α exp −(2π 2 ξ a2/α /(α sin(2π /α)))s2/α , where ξ = K k=1 λk Pk . To obtain the CDF, the inverse Laplace transform of LPH (s) is required: 6 FPH (t) = 1 −

∞

0

(

1 exp(−ut) πu

)   2π 2 ξ a2/α 2/α 2π 2 ξ a2/α 2/α × exp − u u sin du. α tan(2π /α) α

(8.3)

Note that equation (8.3) cannot be obtained in a closed form for a general pathloss exponent; however, it can easily be evaluated numerically. Furthermore, a closed-form expression for the integral in (8.3) exists when α = 4. In this case, the CDF of the aggregate amount of energy harvested by a typical user in one time slot can be obtained as    π 2ξ a , t ≥ 0. (8.4) FPH (t) = erfc 4 t •

Analysis of uplink transmission power. According to the system model described, users served by a BS from tier k are assumed to perform channel inversion in order to satisfy a power level requirement ρk at the serving BS. Thus, we define the required amount of transmit power of a user when it associates with a BS from the kth tier as γk = ρk Rα , where R is the distance to the serving BS from tier k. With the association criterion defined in (8.1), using the superposition property of PPPs and the PDF of R as follows: fR (r) =  probability, we can obtain  the null  2π r exp −π r2 , r ≥ 0, where  = K k=1 λk . Now, the CDF and PDF of the user’s transmit power can be obtained as (  2/α ) t Fγk (t) = 1 − exp −π  , t ≥ 0, (8.5) ρk

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2π  fγk (t) = αρk •

8.4.3



t ρk

2/α−1

(



t exp −π  ρk

2/α ) ,

t ≥ 0.

(8.6)

Transmission probability. The transmission probability of a user associated with the kth tier can be expressed as ηk = P[PS (T) > γk ]. The time-varying nature of the link quality between the BSs and the tagged user directly affects the amount of energy harvested during each time slot. Consequently, it affects the number of time slots To required to charge the battery with sufficient power (energy) to perform channel inversion (i.e., γk ). Hence, To is a random variable that represents the number of time slots required to harvest energy before each transmission and depends both on the required amount of transmit power and on the amount of energy harvested since the last transmission.

Method to Obtain the Boundary Crossing Probability We propose a different method that requires approximating the discrete random walk that can be modeled by a finite state Markov chain. In other words, we discretize the states of the battery into a finite number of levels so that the state space S can be described as a finite set. Note that the stochastic process exhibits the Markov property such that the battery state for a given time slot depends only on the level for the previous time slot, i.e., P[PS (T) > sT ] P[PS (T − 1) > sT−1 ], . . . , P[PS (T − To ) > sT−To ] = P[PS (T) > sT ] P[PS (T − 1) > sT−1 ]. The accuracy of the approximation depends on the number of levels. Therefore, we define w and L as the resolution (or step size) of the approximation and the total number of levels, respectively, i.e., B = Lw. In order to discretize the random walk, we define two probabilities pi and qi . On the one hand, pi is the probability that the amount of power harvested by a user in a certain time slot is between iw and (i + 1)w W, i.e., pi = P[iw ≤ PH < (i + 1)w] for i = {0, 1, 2, . . . , L − 1} and pL = P[PH ≥ B = Lw]. On the other hand, qi is the probability that the amount of transmit power required by a user in a certain time slot is between (i−1)w and iw W, i.e., qi = P[(i−1)w < γk ≤ iw] for i = {1, 2, 3, . . . , L}. Hence, pi and qi can be expressed as pi = FPH ((i + 1)w) − FPH (iw) and qi = Fγk (iw) − Fγk ((i − 1)w), where FPH (t) and Fγk (t) are given in (8.3) and (8.5), respectively. That is, we round the amount of harvested power down to the nearest level while rounding the required amount of transmit power up to the nearest level. Using pi and qi along with the harvest-then-transmit policy discussed above, we can construct the state diagram of the Markov chain and the transition probability matrix P, where Pi,j is the one-step transition probability from state i to state j. Note that in this model the battery has a total of L + 1 distinct states (power levels) such that the lth state denotes a battery level of lw W, i.e., S = {0, 1, 2, . . . , L}. In order to perform the steady-state analysis, we define v = [v0 v1 . . . vL ] as the steady-state probability vector (or the stationary distribution), where vl is the probability  of the Markov chain being in state l and Ll=0 vl = 1. Hence, v = vP, and 1 = v1, where 1 = [1 1 . . . 1] is an all-ones column vector of length L + 1. In order to obtain vl , we need to solve the above system of linear equations. Note that P is an

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 (L + 1) × (L + 1) transition probability matrix, the rank of P is L, and Lj=0 Pij = 1. In order to reduce the solution complexity, we use the Sheskin algorithm to obtain the steady-state probabilities while avoiding matrix inversion and multiplication [22]. In this algorithm, the steady-state probabilities are obtained recursively, where the size of the matrix is reduced iteratively by using only additions and multiplications of some of the matrix elements. Then, the vector v is calculated by using the reduced matrix and some saved values from each iteration. The algorithm is summarized below and the details can be found in [22]. Algorithm 8.1 The Sheskin algorithm to obtain the steady-state probability vector Initialization: Pn = P, k0 = 1 for n = 1 to L Pi,L−n ← Pi,L−n /(1 − PL−n,L−n ), 0 ≤ i < L − n, Pi,j ← Pi,j + Pi,L−n PL−n,j , 0 ≤ i, j < L − n, save last column of Pn end for n = 1 to L n−1   Pi,n ki kn = i=0

end vi = ki /

L 

ki ,

0 ≤ i ≤ L.

j=0

Using the fact that the user is transmitting when she transits to a lower state in the Markov chain model (i.e., the lower triangle of the transition matrix P), we can obtain the transmission probability ηk and the corresponding steady-state vector. That is, for a user served by a BS belonging to the kth tier, the probability that the amount of energy stored in the battery is sufficient to perform channel inversion uplink power control at the beginning of a certain time slot is given by ηk =

L 

vi

i=1 (a)

= 1−

i  j=1

L  i=1

qj (



iw vi exp −π  ρk

2/α ) ,

(8.7)

where (a) follows the definition of qi .

8.5

Discussion We use the results presented so far in order to make some important remarks and extend our framework. The main remarks can be summarized as follows [18]. •

As a generalization for the transmission model, we can adopt a more general harvest-then-transmit strategy in which the user harvests energy for N consecutive

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time slots instead of only one and then checks whether the battery has sufficient energy to perform channel inversion power control. Then, if the energy is sufficient, the user transmits; otherwise, she harvests for another N time slots, and so on. The same results can still be used except that pi should be modified as follows:       a π 2 Nξ π 2 Nξ a pi = erfc − erfc , (8.8) 4 (i + 1)w 4 iw

•

where (8.8) follows because the summation of N identical Lévy-distributed random variables with location parameter of zero is also Lévy-distributed with a location parameter of zero and the scaling parameter is multiplied by N. In the system model, a simple power consumption model that considers only the required RF transmit power (i.e., γk ) is used. However, in practice, a better model should be used to account for other sources of power dissipation in the user’s device, such as the processing power and the inefficiency of RF amplifiers. For example, we can use the following power consumption model: γktot = bγk + Pproc ,

(8.9)

where γktot is the total power consumption in the user’s device, Pproc is a constant that includes all the processing power, and b ≥ 1 is the inefficiency of the RF power amplifier. The effect of using this power consumption model can be captured in (8.5) and the CCDF of PT can be obtained as follows:  1, $ t < Pproc ,   tot  2/α % P γk > t = (8.10) exp −π  (t − Pproc )/(bρk ) , t ≥ Pproc . to be updated accordingly. By defining some integer constant c1 = Thus, qi needs 8 7 Pproc /w , we can express qi as follows:  0, i < c1 , qi = (8.11) i ≥ c1 , Fγk ((i − c1 )w) − Fγk ((i − c1 − 1)w), •

where "x# denotes the smallest integer not less than x. Although the analysis is performed for transmission with channel inversion power control, the results could be suited to other transmission schemes. For example, assume that the user has an intended receiver at a fixed distance, e.g., device-todevice communication and wireless sensor networks. In this case, the user will transmit with a fixed level of power and consume a total power of  that includes the processing power. Let us define an integer constant c2 = "/w#. That is, the user transmits the next data packet if and only if the battery is in state l ≥ c2 , and the battery level will go back to the (l − c2 )th level after transmission. Hence, the entries of the transition matrix P vary according to the following definition of qi :  1, i = c2 , qi = (8.12) 0, i = c2 ,

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•

•

•

279

c2 −1 and the transmission probability is given by ηk = 1 − i=0 vi . It is worth mentioning that this assumption with fixed power transmission has been used in the literature, such as in [23–25]. This system model can also be extended for scenarios in which each user harvests RF energy from a dedicated (fixed) power source(s). That is, assuming that a user harvests energy from a source at a fixed distance rh with transmit power Ph , the amount of power harvested PH will be constant and equal to aPh rh−α . In other cases, e.g., as in [25], PH may also be used as a lower bound on the amount of energy harvested such that a user can harvest energy only when she is inside a disk of radius rh centered at the energy source. Another scenario is to assume that the amount of energy harvested in a cellular network is equal to the mean value of PH . That is, under the assumption of a bounded path-loss model (e.g., min(1, x−α )), the average value of PH can be derived as in [20, Chapter K 3] as3 E[PH ] = k=1 π αPk λk /(α − 2). Note that this assumption is used in [23, 25]. Now, in order7to use our 8 framework under this assumption, we define an integer constant c3 = aPh rh−α such that the battery level goes c3 levels up for each EH time slot. In this case, pi can be expressed as follows:  1, i = c3 , pi = (8.13) 0, i = c3 . An interesting case arises when the battery goes back to state 0 after each transmission (i.e., the user uses all stored energy for transmission once sufficient energy has been harvested). In this case, a closed-form expression for the transmission probability can be obtained. The unnormalized steady-state probabilities ki (see Algorithm 8.1) for this case can be expressed as follows: ⎧ ⎪ 1, i = 0, ⎪ & ⎪  2 ' ⎪ i−1 ⎪  α ⎪ ⎪ pi−j exp −π  ρjwk kj ⎪ ⎪ ⎪ j=0 ⎪ ⎪ ⎪ 1 ≤ i < L, & ⎪  2 ' , ⎪ ⎨ iw α 1 − p0 exp −π  ρk (8.14) ki = & ⎪ 2'   ⎪ L−1 ⎪  jw α ⎪ ⎪ kj ⎪ ⎪ j=0 pL−j exp −π  ρk ⎪ ⎪ ⎪ i = L. ⎪ & ⎪  2 ' , ⎪ α ⎪ B ⎪ 1 − exp −π  ρk ⎩ Then, vi can be obtained by normalizing the values of ki and the transmission probability can be calculated by using (8.7). Note that having sufficient energy stored in the battery does not mean that a user can establish a successful connection with the serving BS. That is, a user might be able to invert the channel toward her BS; however, the received SIR at the BS might be below the level required for a successful decoding of the signal received.

3 For the unbounded path-loss model x−α , the average received power becomes infinite due to the

singularity at (0, 0).

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In this case, the user is said to be in SIR outage. Thus, the coverage (outage) probability is a very important performance metric that should be analyzed. In the following section, we characterize the uplink SIR at a typical BS located at the origin, and then derive closed-form expressions for the uplink coverage probability.

8.6

Uplink Coverage Probability The uplink SIR coverage probability of the kth tier is defined as the probability that the received SIR at a BS in this tier is higher than a predefined threshold τk . Note that we assume the network to be operating in an interference-limited environment. Thus, the SIR coverage probability offered by the kth tier can be mathematically defined as Ck = P [SIRk > τk ] ,

(8.15)

where SIRk is the SIR received at a typical BS belonging to the kth tier. By applying the association criterion defined in (8.1), SIRk used in (8.15) can be defined for a typical BS located at the origin as SIRk = K  j=1

ρk h −α ui ∈ j \{uo } γj gui 

,

(8.16)

where h and g are the small-scale fading coefficients between the typical BS and its served user uo and its interfering users, respectively. k is a point process with density ηk λk that represents the set of active users at a certain time slot, where the term “active users” refers to users who have sufficient energy stored in their battery and ready for transmission. Note that, in general, k is not a PPP; however, for analytical tractability, we assume that the active users at a certain time slot constitute a PPP. This assumption has been used and validated in the literature, e.g., in [16, 17]. Using the instantaneous SIRk given in (8.16) and the definition in (8.15), we can obtain the coverage probability offered by the kth tier in an uplink cellular network for a generic user as & & '' K τk  P [SIRk > τk ] = EI P h > Ij ρk j=1

(b)

=

K

j=1

 LIj

τk ρk

 ,

(8.17)

 −α is the aggregate interference resulting from users where Ij = ui ∈ j \{uo } γj gui  served by the jth tier and (b) follows the definition of the Laplace transform. Let the distance between the closest interfering user from the jth tier j and a generic BS from the kth tier k be denoted by zj , and let its transmit power be γj . We know for Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:08:00, subject to the Cambridge Core terms of use, available at .009

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sure that the average interference received at the BS from tier k is strictly less than ρj . Hence  1/α γj . (8.18) zj > ρj By definition, & LIj (s) = Ej ,{g},γj

$ %' −α exp −sγj gRi k

ui ∈ j \{uo } ∞

& 6 = exp −2π ηj λj

zj

&

Eγj

r dr 1 + (sγj )−1 rαk

'' ,

(8.19)

where zj is the distance from the closest interfering user defined in (8.18). Now, letting uαk = (1/(sγj rαk )), we obtain ( ) $ %6 ∞ u 2/α 2/α du . (8.20) LIj (s) = exp −2π ηj λj s Eγj γj α (1/(sρj ))1/α 1 + u ∞ Note that the 2/α-moment can be obtained as 0 t2/α fpk (t)dt, then, by making the replacement u = t2/α and performing the integration. Hence, % ρ 2/α $ 2/α = k . E γk π

(8.21)

By plugging (8.21) and (8.20) into (8.17), we can obtain the coverage probability as ⎡ ⎤ (   1/α ) K  ηj λj ρj 2/α ρ 1 k F ,α ⎦, (8.22) Ck = exp ⎣−2 τk  ρk τk ρj j=1

∞

where F[y, α] = y (u/(1 + uα ))du. This integration can be evaluated numerically. It reduces to simple closed-form expressions for some special values of α [26, Appendix 3]. As a special case, assume that all BSs in the different network tiers have the same receiver sensitivity. Then, the coverage probability in (8.22) reduces to $ %% $ 2/α −1/α ,α . (8.23) C = exp −2τk ηF τk For ρk = ρ, this result shows that the coverage probability of a multi-tier network depends only on the sum and power-weighted sum of all intensities (i.e.,  and ξ ) rather than on the density of a specific tier.

8.7

Numerical Results and Discussion As we have mentioned before, a user can establish a successful communication link with its serving BS under two conditions.

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1.

2.

The amount of energy stored in the battery of this user is greater than the amount of transmit power required in order to perform channel inversion toward the corresponding BS. The probability that this condition holds true (i.e., transmission probability ηk ) has been discussed in Section 8.4.2 and derived using Markov chain modeling as expressed in (8.7). The level of the SIR received at the serving BS is greater than a predefined threshold (i.e., τ ) in order to guarantee an acceptable quality of service. The probability of this event is referred to as the coverage probability and discussed in Section 8.6, where a closed-form expression has been obtained in (8.22).

Therefore, we define the success probability as the probability that both of the aforementioned conditions are satisfied. That is, success probability = ηk × Ck .

(8.24)

We present typical performance results obtained from the proposed framework for K-tier cellular uplink networks with EH. We focus on the tradeoffs among the different metrics such as the transmission probability (ηk ), SIR coverage probability (Ck ), and success probability of a user associated with the kth tier. In addition, we show how the different network parameters (e.g., the spatial density of BSs, the sensitivity of the BSs’ receivers, etc.) affect the performance metrics. The network scenario under consideration is composed of three different tiers of BSs. In this system, tiers 1, 2, and three denote the macro tier, the pico tier, and the femto tier, respectively. Unless stated otherwise, the transmit powers of BSs are assumed to be P1 = 53 dBm, P2 = 33 dBm, and P3 = 23 dBm, while the thermal noise is ignored (i.e., we consider the interference-limited scenario). The spatial densities of the network tiers are λ1 = 5(0.52 π )−1 BS/km2 , λ2 = 5λ1 , and λ3 = 10λ1 . An independent and identically distributed Rayleigh fading with unit mean is considered for all links and the path-loss exponent is α = 4. The battery capacity is assumed to be 27 dBm and the number of levels used for approximating the battery state by a Markov chain is 5 × 103 . The power conversion efficiency a is set to 1 and the SIR threshold τ is set to 1 (i.e., 0 dB). It is worth mentioning that the effect of RF-to-DC conversion inefficiency (i.e., when a < 1) is equivalent to increasing the receiver’s sensitivity by a factor of a−1 . That is, varying a only scales the resulting figures when plotted against ρk . The simulation parameters are summarized in Table 8.2. Table 8.2. Simulation parameters [18] Parameter

Value

BSs’ transmit powers BSs’ densities (×(0.52 π )−1 ) Battery capacity No. of battery levels SIR threshold Path-loss exponent

53, 33, 23 dBm 1, 5, 10 BS/km2 27 dBm 5 × 103 1 4

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Figure 8.4 Transmission probability, coverage probability, and success probability of a

macro user versus spatial density of BSs (for K = 3, λ2 = 5λ1 , λ3 = 10λ1 , and ρ1 = ρ2 = ρ3 = −90 dBm).

Figure 8.4 illustrates the effect of varying the spatial density of BSs λk on the transmission probability, coverage probability, and success probability. It is worth mentioning that increasing the spatial density results in the three following consequences. 1. 2. 3.

It reduces the distance between the user and the BS serving it, which in turn lowers the required transmission power. It increases the amount of energy harvested due to both the reduction in distance and the increase in the number of available power sources (i.e., BSs). The users experience higher interference due to the increase in the density of the transmitters (i.e., the density of the point process k , which is equal to ηk λk ). In addition, the interferers become closer. This increase in interference degrades the SIR level at the receiving BS since the useful signal level is always constant (i.e., ρk ).

Consequently, as can be seen in Figure 8.4, while the coverage probability Ck starts to fall with increasing λk , the transmission probability ηk improves. However, for a low density of BSs, it can also be seen that the improvement in ηk dominates over the deterioration of Ck and the overall success probability increases. This happens up to some point after which deploying more BSs does not have a significant effect on the overall performance, where both Ck and ηk become almost constant. This behavior can be explained as follows. When the spatial density becomes very high, the expected amount of transmit power becomes very low (see the first moment of γk in (8.21)), whereas the energy available for harvesting becomes very high. The combined effect is that the transmission probability ηk approaches 1. Furthermore, when ηk → 1, the coverage probability Ck becomes independent of λk and approaches a constant level (see (8.22) and (8.23)). Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:08:00, subject to the Cambridge Core terms of use, available at .009

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Figure 8.5 Transmission probability, coverage probability, and success probability of a macro

user versus BSs’ receiver sensitivity (for K = 3 and ρ2 = ρ3 = −90 dBm).

On the other hand, Figure 8.5 shows the effect of varying ρk on the system performance under the same network configuration. Intuitively, decreasing the sensitivity of the receiver (i.e., increasing ρk ) increases the transmission power required in order to perform channel inversion. This, in turn, increases both the level of the useful signal and the interference power received at the BS. Hence, as shown in Figure 8.5, while the coverage probability Ck improves with increasing ρk (see (8.22)), the transmission probability ηk deteriorates (see (8.4)–(8.6)). Regarding the overall performance, it can be seen that there exists an optimal value of ρk that maximizes the success probability and divides the performance into two regimes. That is, as ρk increases, the success probability of a user increases up to a maximum value, whereafter it starts to decrease. The behavior of the system in this case can be explained as follows. When ρk is very low (the left side of the optimal point), although the user can achieve a high transmission probability, the coverage probability is almost 0. As ρk increases, ηk stays almost the same while the SIR coverage improves, and this increase in Ck dominates the success probability. This happens until the maximum success probability has been achieved. After this point, as ρk increases (the right side of the optimal point), ηk starts to fall and the SIR coverage becomes almost constant. Hence, the overall success probability starts to decrease. It has been shown in Figure 8.4 that increasing the spatial density of the network will not be beneficial to the success probability after some point for the same network configuration. However, Figure 8.5 has shown that optimizing ρk can maximize the system performance in terms of the success probability. Therefore, in Figure 8.6 we show how to exploit the deployment of more BSs in order to improve the overall performance of the network. Compared with Figure 8.4, Figure 8.6 shows the maximum achievable success probability on increasing the spatial density of the BSs and Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:08:00, subject to the Cambridge Core terms of use, available at .009

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Figure 8.6 Maximum success probability and the optimal receiver sensitivity versus spatial

density of BSs (for K = 3, λ2 = 5λ1 , λ3 = 10λ1 , ρ2 = ρ3 = −90 dBm).

Figure 8.7 Feasibility region of the two network parameters λk and ρk for different SIR coverage

probability constraints (for K = 3, λ2 = 5λ1 , λ3 = 10λ1 , and ρ1 = ρ2 = ρ3 = ρk ).

optimizing the sensitivity of the BS receiver accordingly. For example, a network with a spatial density of λ1 = 10 × (0.52 π )−1 BS/km2 can achieve a success probability of 82% when optimizing ρk (i.e., −77 dBm) compared with only 45% with the same density of BSs and −90 dBm sensitivity as shown in Figure 8.4. Figure 8.7 shows the feasibility region of the network parameters under some SIR coverage probability constraints. In this case, the feasibility region B is defined as B = {(λk , ρk ) ∈ R2+ | Ck ≥ β},

(8.25)

where β is the target SIR coverage probability. It can be seen that the coverage probability exhibits an opposite behavior to that of the transmission probability as shown in Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:08:00, subject to the Cambridge Core terms of use, available at .009

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Figure 8.5. That is, for the same receiver sensitivity, increasing the spatial density of the BSs degrades the coverage probability. In addition, for the same spatial density, increasing the receiver sensitivity threshold improves the coverage probability. This behavior of the network, shown in Figure 8.5, highlights the tradeoff between these two performance metrics. In addition, it gives design guidelines and shows the importance of selecting appropriate values of the network parameters.

8.8

Summary We have discussed the primary challenges in the deployment and operation of RFbased ambient EH networks. These challenges include non-deterministic energy arrival patterns, EH mode selection, energy-aware cooperation among BSs, etc. A brief review of the existing literature has then been provided to highlight the research gaps and possible future research directions. To this end, a performance analysis model for a Ktier RF EH uplink cellular network has been presented. Using this model, the effects of the different network parameters such as the spatial density of BSs and receiver sensitivity on the user performance (e.g., SIR coverage probability) can be analyzed. Simulation results have shown that the advantage of using RF can be greatly improved with proper choices of the network design parameters. Potential future research directions include consideration of the full-duplex mode of communication in the different network tiers, different radio transmission and propagation scenarios (e.g., considering millimeter-wave communication, SWIPT, directed energy/data transmission), as well as uncertainty in the propagation channels in modeling and analysis of multi-tier EH cellular networks. Radio resource and interference management in multi-tier cellular networks in the presence of ambient EH is another promising area of research.

References [1] E. Hossain, M. Rasti, H. Tabassum, and A. Abdelnasser, “Evolution toward 5G multitier cellular wireless networks: An interference management perspective,” IEEE Wireless Communications, vol. 21, no. 3, pp. 118–127, June 2014. [2] H. Tabassum, E. Hossain, A. Ogundipe, and D. Kim, “Wireless-powered cellular networks: Key challenges and solution techniques,” IEEE Communications Magazine, vol. 53, no. 6, pp. 63–71, June 2015. [3] A. Ghazanfari, H. Tabassum, and E. Hossain, “Ambient RF energy harvesting in ultradense small cell networks: Performance and trade-offs,” IEEE Wireless Communications, arXiv:1512.03122, to appear. [4] W. Ni and X. Dong, “Energy harvesting wireless communications with energy cooperation between transmitter and receiver,” IEEE Transactions on Communications, vol. 63, no. 4, pp. 1457–1469, April 2015. [5] T.-Q. Wu and H.-C. Yang, “On the performance of overlaid wireless sensor transmission with RF energy harvesting,” IEEE Journal on Selected Areas in Communications, vol. 33, no. 8, pp. 1693–1705, August 2015. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:08:00, subject to the Cambridge Core terms of use, available at .009

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[6] I. Flint, X. Lu, N. Privault, D. Niyato, and P. Wang, “Performance analysis of ambient RF energy harvesting with repulsive point process modeling,” IEEE Transactions on Wireless Communications, vol. 14, no. 10, pp. 5402–5416, October 2015. [7] X. Lu, I. Flint, D. Niyato, N. Privault, and P. Wang, “Performance analysis of simultaneous wireless information and power transfer with ambient RF energy harvesting,” in Proc. IEEE Wireless Communications and Networking Conference (WCNC), March 2015, pp. 1303–1308. [8] L. Liu, R. Zhang, and C. K. Chua, “Wireless information transfer with opportunistic energy harvesting,” IEEE Transactions on Wireless Communications, vol. 12, no. 1, pp. 288–300, January 2013. [9] W. Chung, S. Park, S. Lim, and D. Hong, “Spectrum sensing optimization for energyharvesting cognitive radio systems,” IEEE Transactions on Wireless Communications, vol. 13, no. 5, pp. 2601–2613, May 2014. [10] S. Lee, R. Zhang, and K. Huang, “Opportunistic wireless energy harvesting in cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 9, pp. 4788– 4799, September 2013. [11] K. Huang, “Spatial throughput of mobile ad hoc networks powered by energy harvesting,” IEEE Transactions on Information Theory, vol. 59, no. 11, pp. 7597–7612, November 2013. [12] H. S. Dhillon, L. Ying, P. Nuggehalli, P. Zhouyue, and J .G. Andrews, “Fundamentals of heterogeneous cellular networks with energy harvesting,” IEEE Transactions on Wireless Communications, vol. 13, no. 5, pp. 2782–2797, May 2014. [13] M. Maso, S. Lakshminarayana, T. Q. S. Quek, and H.V. Poor, “A composite approach to selfsustainable transmissions: Rethinking OFDM,” IEEE Transactions on Communications, vol. 62, no. 11, pp. 3904–3917, November 2014. [14] H. S. Dhillon, R. K. Ganti, F. Baccelli, and J. G. Andrews, “Modeling and analysis of K-tier downlink heterogeneous cellular networks,” IEEE Journal on Selected Areas in Communications, vol. 30, no. 3, pp. 550–560, March 2012. [15] H.-S. Jo, Y. J. Sang, P. Xia, and J. Andrews, “Heterogeneous cellular networks with flexible cell association: A comprehensive downlink SINR analysis,” IEEE Transactions on Wireless Communications, vol. 11, no. 10, pp. 3484–3495, October 2012. [16] T. D. Novlan, H. S. Dhillon, and J. G. Andrews,“Analytical modeling of uplink cellular networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 6, pp. 2669–2679, June 2013. [17] H. ElSawy and E. Hossain, “On stochastic geometry modeling of cellular uplink transmission with truncated channel inversion power control,” IEEE Transactions on Wireless Communications, vol. 13, no. 8, pp. 4454–4469, August 2014. [18] A. H. Sakr and E. Hossain, “Analysis of K-tier uplink cellular networks with ambient RF energy harvesting,” IEEE Journal on Selected Areas in Communications, vol. 33, no. 10, pp. 2226–2238, October 2015. [19] F. Baccelli and B. Blaszczyszyn, Stochastic Geometry and Wireless Networks: Volume I Theory. Boston, MA: Now Publishers Inc., 2010. [20] M. Haenggi and R. K. Ganti, Interference in Large Wireless Networks. Boston, MA: Now Publishers Inc., 2009. [21] H. ElSawy, E. Hossain, and M. Haenggi, “Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wireless networks: A survey,” IEEE Communications Surveys and Tutorials, vol. 15, no. 3, pp. 996–1019, July 2013. Downloaded from https:/www.cambridge.org/core. Duke University Libraries, on 10 Mar 2017 at 08:08:00, subject to the Cambridge Core terms of use, available at .009

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[22] T. J. Sheskin, “A Markov chain partitioning algorithm for computing steady state probabilities,” Operations Research, vol. 33, pp. 228–235, 1985. [23] K. Huang and V. K. N. Lau, “Enabling wireless power transfer in cellular networks: Architecture, modeling and deployment,” IEEE Transactions on Wireless Communications, vol. 13, no. 2, pp. 902–912, February 2014. [24] K. Huang, “Spatial throughput of mobile ad hoc network with energy harvesting,” IEEE Transactions on Information Theory, vol. 59, no. 11, pp. 7597–7612, November 2013. [25] S. Lee, R. Zhang, and K. Huang, “Opportunistic wireless energy harvesting in cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 9, pp. 4788–4799, September 2013. [26] A. H. Sakr and E. Hossain, “Location-aware cross-tier coordinated multipoint transmission in two-tier cellular networks,” IEEE Transactions on Wireless Communications, vol. 13, no. 11, pp. 6311–6325, November 2014.

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Part III

Applications of Wireless Energy Harvesting and Transfer

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9

Sensor Networks with Wireless Energy Harvesting Xiao Lu

9.1

Introduction Current deployment of large-scale sensor networks either employs miles of cabling for providing electrical power, or battery-powered wireless sensors, which gives rise to a serious environmental problem with the disposal of a huge amount of used batteries [1]. The recent progress in wireless energy transfer and harvesting techniques [2, 3] has provided an alternative way to address the energy limitations of traditional wireless sensor networks. In this chapter, the strategies of energy replenishment for wireless-powered sensor networks are overviewed in detail. Generally, there are two types of solution, i.e., through static wireless charger deployment and mobile charger dispatch [4]. The existing strategies with regard to the two types of solutions are reviewed and discussed. Then, the hardware design principles for sensor circuits are also outlined. Finally, we introduce wireless energy transfer scheduling designed using centralized and distributed approaches, and future research directions are discussed.

9.2

Static Wireless Charger Deployment In sensor networks, the energy supply is limited. Wireless energy transfer and harvesting techniques have been adopted to supply energy to sensor nodes. In particular, a wireless charger is used in sensor networks to supply energy to multiple sensors simultaneously. Thus, optimal deployment of wireless chargers is an important issue. Wireless charger deployment concerns the planning of charger locations. The goal is to provide sufficient energy to wireless sensors in the network. We can divide wireless charger deployment problems into two categories. The first category is static charger placement, in which case, after having been deployed, the chargers remain at the same locations. The second category is mobile charger placement. The charger can move, and hence the deployment optimizes the path of the charger’s motion. Wireless charger deployment is important because the charging range is limited, e.g., to a few meters for coupling-based wireless chargers and tens of meters for RF-based chargers. Thus, the deployment must be Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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optimized to meet the energy demand of the wireless sensor networks. Especially in a large-scale network, deploying chargers to support all sensor nodes is too costly and has too high an overhead. An efficient method has to be devised [5]. As shown in Figure 9.1, we have four scenarios for existing wireless charger deployment strategies that have been addressed in the literature. • • •

•

Point provisioning [6] allows the placement of static chargers to support static charging devices with wireless power. Path provisioning [6] allows one to deploy static chargers to charge mobile devices. The mobile devices should be located along the chargers’ travel paths. Multi-hop provisioning aims to find the locations at which to place static chargers in a static network. The charging devices in the network are also able to receive wireless energy, and can share energy with each other to improve the network lifetime. Landmark provisioning includes the selection of landmarks for the mobile chargers to visit by turn and clustering of landmarks as groups at which to deploy mobile chargers. The landmarks are the locations at which to locate chargers in order to provide simultaneous wireless charging for multiple static devices nearby.

The first three scenarios are concerned with static charger deployment, while the last one requires mobile charger deployment. In the following two subsections, we review the strategies in these scenarios.

9.2.1

Static Wireless Charger Deployment Most of the related work, including [7–12] has studied the charger deployment problem for the point provisioning case. That is, the charger is deployed at a certain location. For example, the authors of [8] considered a wireless-powered sensor network. The network has wireless chargers to be placed at grid points. At each point, the charger is located at a certain height. The wireless charger has three-dimensional (3D) RFbased beamforming to provide a cone-shaped charging space. This is called a charging cone. To minimize the deployment cost, the number of chargers must be minimized; hence the node-based greedy cone selecting (NB-GCS) algorithm was proposed in [8]. Moreover, the authors extended the NB-GCS and introduced the node-pair-based greedy cone selecting (PB-GCS) algorithm. The NB-GCS and PB-GCS algorithms are able to generate charging cones on a node-by-node and pair-by-pair basis, respectively. The simulation shows that the PB-GCS algorithm achieves better performance than that of the NB-GCS algorithm, i.e., it requires fewer chargers. Moreover, it was discovered that the performance gap between these two algorithms increases as the number of sensor nodes increases. However, the NB-GCS algorithm has significantly lower complexity, especially when the number of nodes is large. Thus, the scalability is higher. By carrying out a comparison with the network model in [8], where only a wireless charger serves as an energy source, the authors of [7] further evaluated this charger deployment problem where randomly deployed base stations coexist. 10 Mar 2017 at 08:08:02, .010

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(a)

293

(b)

Point Provisioning Scenario (c)

Path Provisioning Scenario (d)

Multi-hop Provisioning Scenario

Landmark Provisioning Scenario

Figure 9.1 Reference models of the wireless charger deployment scenario.

The authors of [10] considered the deployment of a finite number of wireless chargers. The chargers are deployed next to each other according to the number of bottleneck sensors. This strategy is to maximize the flow rate of the network. The authors first formulated a mixed integer linear programming (MILP) approach to find the routing and the set of bottleneck sensors to be charged. However, solving the MILP formulation involves high complexity. Therefore, a heuristic algorithm was proposed, i.e., a heuristic charger deployment scheme. The performance evaluation showed that the heuristic algorithm can achieve on average 85.9% of the optimality of the solution generated by the MILP. The authors of [9] studied the problem deploying the minimum number of chargers possible to satisfy the charging coverage requirement for a set of sensors. An optimization formulation was derived, and, to reduce the complexity, the authors introduced an approximation solution. The solution is based on employing a network partition algorithm to choose the deployment locations for wireless chargers. Moreover, the authors analyzed the order of approximation under the condition that all the target sensors are evenly distributed. Then, the authors introduced a shifting strategy, which is able to prove the performance lower bound of the proposed partition algorithm. 10 Mar 2017 at 08:08:02, .010

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The authors of [11] and [12] studied the wireless charging strategy to meet a safety constraint under electromagnetic radiation regulation. In [11], the authors analyze an equivalent problem to the point provisioning of the charger deployment. In particular, given a set of deployed chargers, the authors presented a method by which to select the chargers to be active so that nowhere on the planar field is exposed to electromagnetic radiation exceeding a given limit. As the radiation limit applies everywhere, the problem appears to have an infinite number of constraints. Therefore, the authors showed that searching for an optimal set of chargers to be activated so that the overall charging throughput is maximized is NP-hard in general. To propose a solution, constraint conversion and constraint reduction techniques were applied. It was shown that the original problem can be transformed into two traditional problems. The first problem is the multidimensional 0/1 knapsack problem [13]. The second problem is the Fermat– Weber problem [14]. Then the near-optimal approximation algorithm was proposed as a solution. The algorithm was shown to outperform the particle swarm optimization (PSO)-based heuristic algorithm by 35%. The authors of [12] extended the work in [11] by including the adjustable transmit power of the chargers in the problem instead of on/off operation as in [11]. The objective set was to achieve the highest possible charging utility. The utility is defined proportionally to the total charging power. As in [11], this problem has an unlimited number of constraints. Thus, the authors first reformulated the optimization problem as a conventional linear programming problem by utilizing an area demonetization technique. Although the linear programming problem can be solved efficiently, the authors still aim to reduce the complexity by introducing the distributed redundant constraint reduction approach. The intention is to reduce the number of constraints in the linear programming problem, which causes much complexity. The authors further developed the distributed approximation algorithm. The experiment with a Powercaster testbed showed that the proposed distributed algorithm can achieve an average performance gain of 40% compared with the centralized solution discussed in [11]. The authors of [6] studied both point and path provisioning problems. The system model is the wireless identification and sensing platform. In this system model, the RFID readers recharge RFID tags wirelessly. The point and path provisioning problems both have the same objective, i.e., to minimize the number of chargers required in the network. The authors made the assumption that the recharging power from multiple RFID readers is additive. For the analytical results, the authors obtained the lower bound on the number of readers required for the point and path provisioning problems. Then, the simulation was used to show that, compared with the traditional triangular deployment approach in the sensing disk model [15], the proposed approach for point provisioning resulted in a substantial decrease in the number of chargers. Additionally, the proposed approach for point provisioning was proved to achieve near-optimal performance. More importantly, the proposed method for path provisioning achieves close to optimal performance in a practical system setting. The authors of [6] adopted a similar idea and considered a full-coverage scenario. This scenario is practically suitable for a small network. However, for a large-scale network, it may incur too much complexity and overhead. 10 Mar 2017 at 08:08:02, .010

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While the above works concerned algorithm design, the authors of [5] developed a cost-effective scheme for charger deployment in large-scale networks. In particular, the authors use the idea of partial coverage in a path provisioning scenario. This idea is based on the observation that human movement has some degree of regularity [16]. The problem is formulated and its objective is to obtain a mobility-aware deployment scheme that is able to achieve a desirable survival rate with a limited number of available chargers. The authors formulated the mobility-aware charger deployment (MACD) problem for the maximum survival rate on a grid-based map. The grid points are basically the potential locations at which to site the chargers. The authors proved that the MACD problem is NP-hard. To overcome this limitation, the authors designed a lowcomplexity MACD algorithm based on the greedy method. The authors conducted a simulation showing that the performance of the proposed MACD algorithm is superior to that of the full-coverage scheme in [6]. Specifically, the proposed MACD algorithm achieves the same survival rate with substantially fewer chargers. This is done by making effective use of the regularity of the end-devices’ mobility. The above works considered only one-hop wireless charging networks. In such networks, all of the wireless power is directly transferred from the chargers to the nodes. Instead, the authors of [17] considered a multi-hop wireless network with charger provisioning. Each node in the network can not only receive, but also transmit, energy to its neighbors. In this network setting, the authors formulated an optimization problem to minimize the number of chargers of fixed capacity as an MILP problem. The formulated problem has a constraint on the maximum number of hops for energy transfer. By simulation, the authors compared the proposed solution with a single-hop charging approach. It was shown that the proposed solution requires for fewer chargers. This is especially so when the charger capacity is large. However, for multi-hop charging, the tradeoff between charging efficiency and number of hops must be analyzed.

9.2.2

Mobile Wireless Charger Deployment In mobile wireless charger deployment, the chargers can move in order to charge distributed nodes. The authors of [18] introduced a novel three-step scheme, called SuReSense. The scheme was designed to solve the deployment problem for multiple mobile wireless chargers in a wireless-powered sensor network. First, the authors introduced an integer linear programming (ILP) problem. The objective is to minimize the number of landmarks, i.e., the points that the mobile charger will pass, depending on the location and power demand of the sensors. The authors allow the landmarks to be grouped as clusters in terms of their proximity to docking stations. A docking station is a static point that recharges mobile chargers. Finally, each mobile charger visits the landmark following the shortest Hamiltonian cycle. The proposed shortest Hamiltonian cycle was compared with a scheme in which the wireless charger visits each sensor individually according to the landmarks. The simulation results indicated that SuReSense is able to achieve a shorter path length, especially when the power demand of the nodes is not too great. 10 Mar 2017 at 08:08:02, .010

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Motivated by the work in [18], the authors of [19] and [20] studied the landmark selection. The selection is performed to achieve different objectives. The work in [19] considered the profit maximization problem [21] in a wireless-powered sensor network with mission assignment [22]. To obtain the maximum profit possible, the authors introduced an ILP model called mission-aware placement of wireless power transmitters. The model is used to determine the maximum number of devices charged from each landmark. The simulation showed that the profit can be significantly improved by limiting the number of landmarks. Moreover, it was found that the profit decreases when the number of missions increases. This is due to the fact that, to complete more missions, the nodes must be charged from more landmark locations, increasing the chance of energy outage. The authors of [18] and [19] considered only the case that all nodes have the same priority. However, in practical sensor networks, this need not be true. For example, sensors in some critical areas, e.g., those close to the target, need to perform more precise monitoring. These nodes will need more power provisioning. To address this issue, the authors of [20] proposed a strategy called differentiated RF power transmission (DRIFT). The strategy was developed by extending the work in [18] by incorporating different priorities of the sensor nodes. The ILP model was again developed. Its objective is to maximize the amount of energy delivered to the high-priority nodes from each landmark. In the performance evaluation, the simulation showed that the DRIFT strategy allows the high-priority nodes to receive a significantly higher amount of energy, sustaining their operation substantially. However, compared with the works in [18] and [19], SuReSense generates a shorter path length for the mobile charger. Additionally, the authors proved that there exists a tradeoff between the power reception efficiency and the path length.

9.2.3

Discussion and Summary Table 9.1 shows a summary of existing wireless charger deployment strategies. We observe that multi-hop provisioning has been less thoroughly investigated, having been examined only in [17]. Furthermore, it is important to study the network when each node can harvest energy from multiple chargers. Insofar as for the deployment scenarios are concerned, none of the existing works considers the deployment of mobile chargers in mobile networks, e.g., ad-hoc networks. The mobile charger deployment strategies should also take the mobility patterns of users and nodes into account. It is worth noting that the deployment problems are mostly formulated as optimizations. The objective and constraints are different for different formulation. Because of the need for optimization, in order to obtain an optimal solution, global information including specification of the set of devices, the devices’ battery capacity, mobility, and location, and even hardware specification (e.g., in [5]) is required, which can be expensive to obtain. Moreover, obtaining the global information incurs substantial computation and communication overhead. One possible solution is to develop a lowcomplexity and scalable algorithm for a large network, e.g., [5] and [18]. This may cause 10 Mar 2017 at 08:08:02, .010

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Table 9.1. Summary of wireless charger deployment strategies Reference

Scenario

Objective

Constraint

Solution

[7]

Point provisioning

Location limit and number limit of energy transmitters

Centralized solution based on ILP

[5]

Point provisioning Point provisioning Point provisioning

Maximization of power transferred and minimization of number of BSs and energy transmitter Minimization of number of chargers Maximization of system flow rate Minimization of number of chargers

Network charging coverage requirement Limitation on Number of wireless chargers Network charging coverage requirement

[11]

Point provisioning

Maximization of charging throughput

Electromagnetic radiation limit

[12]

Point provisioning

Maximization of charging throughput

Electromagnetic radiation limit

[6]

Point provisioning, path provisioning Path provisioning

Minimization of number of chargers

Average charging rate requirement

Two centralized greedy algorithms Centralized solution based on MILP Centralized approximation solution Centralized approximation solution Distributed approximation solution Centralized solution based on non-linear optimization

Maximization of survival rate

Limitation on number of chargers

[17]

Multi-hop provisioning

Minimization of number of chargers

[18]

Landmark provisioning

Minimization of number of landmarks

[19]

Landmark provisioning

Maximization of mission profit

[20]

Landmark provisioning

Maximization of power delivered to high-priority nodes

Network coverage requirement, maximum limit of hop number for energy transfer Total energy replenishment demand, capacity limit of chargers Energy replenishment demand, capacity limit of charger Maximum number of landmarks, transmission range limit and power requirement of high-priority nodes, capacity limit of charger

[10] [9]

[8]

Centralized heuristic greedy algorithm Centralized solution based on mixed ILP

Centralized solution based on ILP

Centralized solution based on ILP Centralized solution based on ILP

the network performance to deteriorate. Furthermore, the feasibility and practicability of such low-complexity algorithms in the real system have to be assessed. Another common approach is based on decentralized algorithms, which use only local information, thereby decreasing the complexity and overhead. Finally, system level simulations to evaluate the performance of the network in all aspects must be conducted, e.g., as in [6] and [8]. The simulations will provide insights that will be useful for designing 10 Mar 2017 at 08:08:02, .010

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a practical network to meet the requirements. Then, experiments on the actual system will establish the empirical performance.

9.3

Mobile Sensor Charger Optimization From this section, we review the network applications of wireless charging for sensor networks. We classify the work into mobile charger dispatching, static charger scheduling, and wireless charger deployment. The mobile charger dispatch problem is that of how to determine and schedule the travel of one or multiple mobile chargers. The objective is to let them visit and recharge a group of devices through wireless energy harvesting and transfer. The design goal is to achieve a long network lifetime. Typically, the mobile charger dispatch problem is mostly evaluated with wireless-powered sensor networks [23]. Generally, the following issues must be addressed in charger dispatch problems. •

•

• •

•

The best charging locations for a mobile charger to visit must be obtained for a given number of distributed devices and their locations. The constraint is that wireless charging must supply enough energy to all the devices. An optimal travel path (sequence) for the charger to visit all the locations must be determined for a given number of charging locations for a mobile charger to visit. Again, the constraint is that one must supply enough energy to the entire network. An optimal charging duration for the charger to stay at each location must be obtained for a given number of sojourn locations for a mobile charger to visit. The best data flow rates and data routing paths for the devices must be obtained for a given number of devices, their locations, and a data flow requirement. The goal is to maximize the overall data gathering performance. Multiple chargers can perform collaborative energy provisioning. In this case, the minimum number of chargers to be deployed to meet a certain objective, e.g., the minimum cost, must be obtained.

To address the above issues, the problems can be generalized to the optimization of the charging location, travel path, charging time, data rate, routing path, and number of chargers. Figure 9.2 shows two general system models that have been considered in the literature for mobile charger dispatch planning and scheduling. For the first model, as shown in Figure 9.2(a), wireless charging is performed by the mobile charger(s). Meanwhile, data gathering is executed by a data sink or an access point. Therefore, the data flow routing and energy consumption rate of network devices are independent of the charger mobility. Typically, a charger is located at a service station or a data sink and moves to other devices in the network. After visiting the devices, the charger moves back to the service station again to re-charge energy stored in its battery. The mobile charger can use point-to-point charging or point-to-multipoint charging techniques, depending on the assumption and system setting. Travel Tour 1 and Travel Tour 2 in Figure 9.2(a) show 10 Mar 2017 at 08:08:02, .010

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(a)

Separated wireless energy provisioning and data gathering (b)

Joint wireless energy provisioning and data gathering Figure 9.2 Reference models of mobile charger dispatch.

examples of point-to-point charging and point-to-multipoint charging, respectively. In general, the point-to-multipoint charging scenario is more commonly used. In this case, the charger at a selected landmark location, which is also called an anchor point, can transfer energy to multiple devices within its charging range simultaneously [24, 25]. For the second model, as shown in Figure 9.2(b), a hybrid charger is deployed. The hybrid charger can perform both data collection/forwarding and wireless power transfer. Data can be forwarded to the hybrid charger when the charger visits a charging location. The data transfer can be done in a single-hop or multi-hop fashion, shown as routing path 1 and routing path 2 in Figure 9.2(b). It is important to note that mobile data collection in wireless sensor networks has been studied extensively. Literature surveys exist, e.g., [26]. In this second model, wireless energy provisioning and data gathering are jointly optimized, which potentially achieves better wireless energy and data transmission efficiency. If the location of the charger keeps changing, dynamic routing problems have to be solved. 10 Mar 2017 at 08:08:02, .010

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Figure 9.3 Taxonomy of mobile charger dispatch strategies.

A taxonomy of mobile charger dispatch strategies is shown in Figure 9.3. Given the timeliness of energy demand, the strategies can be divided into offline and online dispatch planning. Alternatively, the strategies can be divided into single-charger and multiple-charger types. Depending on the control structure, the mobile charger dispatch strategies can be divided into centralized and distributed approaches, offline and online strategies, as well as ones with a single charger and multiple chargers. We will summarize the strategies in tables and indicate whether each one is centralized or distributed.

9.3.1

Offline Charger Dispatch Strategy Most of the existing work focuses on an offline scenario. In this scenario, the energy transfer scheduling is performed periodically.

9.3.1.1

Single-Charger Strategy Most of the single-charger strategies have the objective of minimizing the total service time of the charger [27–33]. This includes travel and charging times. This objective is equivalent to maximizing the idle or vacation time of a charger [29] and maximizing the ratio between the vacation time and the cycle time of the charger [27]. The objective can be interpreted as minimizing the energy consumption of the charger [32]. In [27], the concept of a renewable energy cycle was introduced. It is observed that the energy level in the battery of a device has some periodicity over a time cycle. The authors defined the necessary and sufficient conditions for a renewable energy cycle to achieve an unlimited network lifetime. Then, the work analytically proved that an optimal travel path for the charger to achieve the renewable energy cycle is the shortest Hamiltonian cycle (SHC). Typically, the shortest Hamiltonian cycle can be achieved by solving the well-known traveling salesman problem (TSP) [34]. This problem is well known to be NP-hard in general. Nevertheless, even though the problem is NP-hard, the optimal travel path for the TSP with thousands of points can be solved efficiently, e.g., by applying the technique in [34] or the tools in [35]. With the optimal travel path obtained from the algorithm, the authors formulated a non-linear optimization problem for joint charging duration and data flow routing. Again, the problem was shown to be NP-hard. To efficiently obtain the solution, the authors adopted a piecewise 10 Mar 2017 at 08:08:02, .010

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linear approximation technique. In particular, the authors derived a feasible solution of the problem. The solution was then validated, e.g., by establishing a near-optimality property, using both a theoretical proof and numerical results. Similarly, in [30], a non-linear programming (NLP) problem was formulated to optimize the travel path, charging duration, and data flow routing jointly. Unlike in [27], where the flow routing was assumed to be invariable, dynamic time-varying flow routing was considered in [30]. To obtain the solution, again, linearization techniques were applied. Next, the authors reformulated the original problem as a linear programming (LP) problem. The problem can be solved within polynomial time, which is more suitable for practical implementation. The simulation results under a realistic setting show that the proposed strategy yields a much larger objective value and incurs lower complexity than that of the static data routing. Moreover, static data routing may result in an infeasible solution. In [31–33], the selection of charging locations was considered. Point-to-point charging was assumed in [27], whereas in [33], which is an extension of [27], point-tomultipoint charging was considered. The authors formulated an NLP problem. The problem was shown to be NP-hard. To obtain the solution, the authors applied discretization and a reformulation linearization technique [36]. In particular, the NLP was first converted to a mixed-integer NLP (MINLP) and then a mixed-integer linear programming (MILP). The solutions of these problems were proved to be near-optimal and came close to the optimal solution with a certain bound. The simulation revealed a significant performance gap between point-to-point and point-to-multipoint charging scenarios. The authors of [31, 32] considered the mobile charger and static base station for wireless energy provisioning and data gathering jointly. In the proposed system model, the data generated from devices will be forwarded to the hybrid charger over multihop connections. The authors of [32] then formulated a time-dependent optimization problem for the dynamic data flow routing. The travel path for the charger was known a priori. A special case that involves only location-dependent variables was considered. It was shown that this special case of the problem has the same optimal objective value. Moreover, it can yield a solution space as a subset of the solution space for the original problem. Thus, a near-optimal solution to the special case problem can be obtained with much lower complexity. The authors of [31] studied the case with an unknown travel path. Unfortunately, solving the problem in this case incurs much complexity. To systematically address the issue, the authors first considered an ideal case of zero traveling time for the charger. The authors further adopted the discretization and logic point representation techniques. They were proved to provide a near-optimal solution. From the solution, the authors also obtained the travel path of the original problem by finding the shortest Hamiltonian cycle which connects all the logical points with non-zero sojourn time. From that travel path, the authors obtained the solution. Moreover, the performance gap between the solution obtained and the optimal solution was analyzed. The authors of [28, 29] proposed path planning strategies. It was assumed that pointto-multipoint charging is adopted. In accord with [33], the authors of [29] adopted the 10 Mar 2017 at 08:08:02, .010

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shortest Hamiltonian cycle as a charger travel path in the proposed strategy. The authors then focused on optimizing the charging duration when the charger is located at each stop. This problem was formulated and solved as a dynamic optimization. Likewise, the authors of [28] formulated a linear programming problem. The decision variable is to determine the charger location and the corresponding duration of charging. It was shown in [28] that the solution space can be reduced substantially, meaning that an optimal solution can be obtained in the smallest possible enclosing space [37] and charging power discretization. Despite the improvement, the authors further reduced the complexity by devising a heuristic algorithm based on k-means clustering. The algorithm, called Lloyd’s algorithm [38], has the ability to merge nearby charger stop locations into a single location. This can maintain the charging delay under the threshold. The simulation results showed that the heuristic algorithm achieves a close-to-optimal performance. More importantly, it clearly outperforms a set-cover-based approach [39]. This approach maximizes the number of under-charged devices near each stop. The authors of [40, 41] studied target-oriented wireless-powered sensor networks. In the network, wireless charging strategies were jointly optimized with sensor activation to monitor a target. In particular, the target monitoring generates the same information regardless of the number of sensors. Thus, sensor activation scheduling is needed in order to coordinate the sensors so as to avoid redundant monitoring and minimize energy consumption. The authors of [40] formulated an optimization problem to maximize the average number of targets monitored. The problem was proved to be NP-complete. Therefore, the authors design a greedy algorithm and a random algorithm to balance between computational complexity and network performance. The numerical evaluation showed that the greedy algorithm achieves comparable performance to that of the random algorithm when the charger has a slow speed. The greedy algorithm outperforms the random algorithm when the mobility speed of the charger is high. The authors of [41, 42] investigated the problem of optimizing the quality of monitoring (QoM) in a sensor network. The QoM metric is defined as the average amount of information obtained per event monitored by the sensor networks. To achieve an optimal performance, the authors of [42] proposed a simple algorithm called joint periodic wake-up (JPW). The algorithm jointly dispatches a mobile charger to visit and charge nearby sensors at points of interest (PoI). The charging is done within a predefined charging duration. The charger can control a duty cycle of the sensors to reduce energy consumption given satisfactory performance. The simulation showed the impact of the charging duration on the quality of monitoring performance. The authors of [41] proposed an optimization problem to maximize the QoM metric. However, the authors showed that the problem is NP-hard. To address this issue, the authors first developed a relaxed problem. The relaxed problem ignores the travel time of the charger. Then, the authors reformulated the relaxed problem as a monotone submodular function maximization problem under a special sufficient condition. The algorithm was designed to achieve an approximation ratio of 1/6 for the relaxed problem. Then, using the results obtained by the approximation algorithm, another algorithm was developed for the original problem. More importantly, the authors obtained the order of approximation and time complexity of the two proposed approximation algorithms 10 Mar 2017 at 08:08:02, .010

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analytically. In a simulation comparing it with the JPW algorithm in [42], the proposed algorithm was shown to provide a significant gain in performance. The authors of [24, 25] aimed to maximize network utility. The utility function is defined in terms of an overall data gathering performance. Specifically, in [25], the authors developed a two-step algorithm for the joint design problem. In the first step, the selection of a subset of sensors to be anchor points was done. In the second step, data gathering when a mobile charger moves among the selected anchor points was optimized. Moreover, the authors implemented the selection algorithm to search for the maximum number of sensors. The algorithm aims to achieve the least energy level for the anchor points. Meanwhile, the tour length of the charger is maintained below a threshold. Then, the authors formulated an NP-hard flow-level network utility maximization problem. A proximal approximation-based algorithm to obtain a system-wide optimal solution in a distributed fashion was developed. The performance evaluation involved a simulation that verifies the convergence of the proposed algorithm and good performance under different network topologies. As an extension of [25], the work in [24] considered energy consumption and timevarying charging duration of heterogeneous devices. The authors formulated the problem by incorporating the constraints on flow conservation, energy balance, link and battery capacity, and charging duration limit. However, the problem was shown to be non-convex. To avoid such a complication, the authors introduced some auxiliary variables. Thus, the original problem was reformulated as a convex optimization problem. To reduce complexity, the problem was then decomposed into two levels of optimization. The decomposed optimization was solved by a distributed cross-layer method. The method adaptively adjusts the device’s optimal data, routing paths, instant energy provisioning status, and charging duration. The objective was to maximize the network utility. The simulation based on NS-2 [43] demonstrated the fast convergence of the proposed algorithm. Moreover, the robustness of the algorithm against the perturbation defined as a small level of node failure was evaluated. The algorithm clearly outperforms the algorithm proposed in [25] in terms of network utility and lifetime. The authors of [45] investigated how to maximize the number of devices that can be charged. The constraint is on the total energy consumption for both traveling and charging of the charger. The authors adopted multiple-node charging, which allows the optimization of charging location selection to reduce the tour length. The problem was shown to be NP-hard. Therefore, a heuristic algorithm based on the meta-heuristic of PSO [46] was introduced. The simulation showed that the PSO algorithm achieved a small gap between the heuristic and optimal TSP solution. Nevertheless, the number of iterations required by the heuristic algorithm to obtain the solution is significantly larger. The above single-charger strategies were all based on the assumption that the mobile charger has sufficient (or infinite) energy capacity to visit and charge an entire network, at least within each tour. However, a more realistic problem is to design charger dispatch strategies for a mobile charger with limited capacity. Thus, the authors of [44, 45] took the energy constraint of the mobile charger into account. The aim of [44] is to find an optimal travel path that the network lifetime is maximized. The authors showed the NP-completeness of the charging problem and designed two heuristic algorithms to 10 Mar 2017 at 08:08:02, .010

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reduce the computational overhead. Within the constraint of a given charger’s battery capacity, the first one attempts to prolong the network lifetime as much as possible, while the second one improves on the first one by employing binary search to find a more suitable target network lifetime.

9.3.1.2

Multiple-Charger Strategy Unlike in the single-charger case, with a multiple-charger strategy, the purpose is to coordinate the dispatch of mobile chargers from a common service station or several distributed service stations. The mobile chargers then visit a group of devices to transfer energy. The multiple-charger dispatch strategy further requires coordination among the mobile chargers. Therefore, the design of a multiple-charger strategy focuses on the minimization of the number of chargers given a charging coverage requirement and the scheduling of the optimal dispatch planning. Most of the multiple-charger strategies have involved point-to-point charging. The authors of [48, 49] studied a one-dimensional (1D) linear wireless-powered sensor network. The charging time was chosen to be negligible in order to simplify the problem. The objective is to minimize the number of chargers able to maintain the operation of the network. In [48], an optimal solution was derived with linear complexity for searching of the minimum number of chargers. The solution was applied also for the dispatch planning in a homogeneous charging scenario. In this scenario, the charging frequency for all devices is the same. For a more realistic case of heterogeneous charging, i.e., different charging frequencies, the authors devised a greedy algorithm. Still, the chargers were assumed to have infinite battery capacity. Unlike in [48], the authors of [49] assumed limited energy storage of the chargers. The different approaches when each sensor is allowed to be charged by a single charger and jointly by multiple chargers were discussed. Also, the case in which mobile chargers are enabled to charge each other was considered. The authors proposed an optimal solution to minimize the number of chargers for the case in which inter-charger charging is allowed. The solution can yield the maximum ratio between the amount of energy consumed for charging and that for traveling. Instead of 1D linear network topology, the authors of [50–52] considered twodimensional (2D) wireless-powered sensor networks with energy-constrained chargers. The authors of [50] presented the optimization problem with the objective of minimizing the number of chargers. However, the problem was shown to be NP-hard. Thus, to solve this problem, the authors adopted an approximation algorithm by relaxing the original problem. The relaxation was done by removing a linear constraint. Then, using the solution obtained from the relaxed problem, the authors implemented two approximation algorithms for the original problem. The order of approximation for both algorithms was derived analytically, which gives some insight into the problem. The simulation clearly showed the advantage of the two proposed approximation algorithms over a baseline algorithm. The authors of [51] formulated a problem to minimize the sum of the traveling distance of all chargers. The problem can be cast as a q-root TSP. The intention was to find q closed tours covering all locations. The tours must have the minimum total 10 Mar 2017 at 08:08:02, .010

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length. However, the problem is NP-hard. Therefore, the authors developed an approximation algorithm. The algorithm was guaranteed a provable approximation ratio of 2. However, this is under the assumption that the energy consumption rates of all devices are constant. The algorithm finds q-root trees with the minimum distance. Then, each tree is transformed into a closed tour, with the length of each tour being no more than twice that of the corresponding tree. Then, the authors considered the case with heterogeneous energy consumption rates. A heuristic algorithm was developed to reduce the complexity. The simulation showed that the proposed algorithm performs better than a greedy baseline algorithm. Similarly, the authors of [52] also proposed a q-root TSP. The purpose was to schedule multiple chargers. At the same time, it can minimize the number of chargers deployed. The problem was solved by a two-step design. In the first step, a tree decomposition algorithm similar to that in [51] with a provable approximation ratio of 5 was introduced to find q closed tours. In the second step, an approximation algorithm that invokes the first algorithm was proposed in order to minimize the number of chargers. The algorithm bounds the total distance of each tour to within a certain value. The performance evaluation was performed for networks with linear and random distributions of energy consumption rate. The proposed algorithm can obtain a performance equivalent tot 40% that of the optimal solution. The authors of [53] incorporated a constraint of the travel time of a charger. The objective was to minimize the total traveling cost. This is given that there is no node outage. To address the problem, the authors formulated a TSP with deadlines. The problem is shown to be NP-hard. To reduce the computational complexity, a heuristic algorithm was proposed. The algorithm selects the nodes to recharge energy according to the weighted sum of the travel time and residual lifetime of sensor nodes. All the above works considered a centralized approach such that the solution is obtained with global information. In contrast, the authors of [54] studied distributed control with local information. The authors proposed to establish a balanced tradeoff between the charging performance and the amount of information required. The authors then introduced two distributed algorithms. In these algorithms, the chargers use information about the status of neighboring chargers to arrange coordination among nearby chargers. The first algorithm does not need complete network information. The second algorithm requires only local knowledge of the network. The simulation shows that the first distributed algorithm achieved a performance close to that of the centralized approach. However, the second algorithm provides better performance.

9.3.2

Online Charging Dispatch Strategy Most of the approaches reviewed in the previous subsection are based on the assumption that the mobile charger operates with offline perfect global knowledge. However, in practice, this assumption might not be valid because collecting global information may cause too much communication overhead and consume a significant amount of energy. Furthermore, the offline strategies might not be able to adapt to the network changes because the information has to be collected a priori. Therefore, in real networks 10 Mar 2017 at 08:08:02, .010

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with variation and uncertainty of network demand and setting, offline charger dispatch strategies are not a suitable choice and can suffer from performance degradation. Thus, an online charging dispatch strategy is considered for real-time charging. The online charging dispatch strategy allows a mobile charger to receive new charging requests at any time instant and to obtain new network information. The online charging dispatch strategy can construct and adjust the travel paths of the chargers on an on-demand basis. In the following, we review online charger dispatch strategies. Most of the authors who have developed online charging dispatch strategies considered single-charger dispatch. The approaches proposed in [55, 56] are based on centralized control. In particular, the authors of [55] formulated a problem to maximize the network charging throughput per travel tour. The authors first considered an offline formulation assuming that all charging requests are completely known. The offline formulation was first shown to be NP-hard. An offline approximation algorithm was devised to solve the problem. Then, the authors considered an online formulation with one-by-one arrival of charging requests. A naive algorithm was proposed to re-plan the travel path iteratively. Specifically, the algorithm always serves the request with the smallest processing time. The processing time is the total traveling time plus charging time. The authors then extended the algorithm by considering the case with point-tomultipoint charging. For this case, the authors proposed a cluster-based algorithm that groups the requesting sensors into different clusters according to their locations. The charger then evaluates and chooses the cluster according to a charging gain. The gain is defined as the energy transfer efficiency for supplying energy to sensors in a group. A heuristic algorithm is used to determine the cluster with the highest charging gain. The authors of [56] developed an energy synchronized charging (ESync) protocol. The protocol was designed to reduce both the travel distance and the charging delay of chargers. The protocol uses on-demand energy provisioning by determining a group of nested TPS tours. The tours are determined by selecting the sensors with low residual energy. To further improve the travel tour, the authors adopted the concept of energy synchronization to achieve a better charging sequence of the sensors. The request sequence is used for the travel tour construction, which depends on the devices in each charging round. The efficiency of the ESync protocol in terms of reducing the traveling distance and charging delay was shown by both simulation and experiment. The authors of [57–59] focused on distributed charging dispatch strategies. In particular, the authors of [57] studied the energy provisioning problem for a circular network with devices uniformly randomly distributed. In contrast to the centralized online charging dispatch strategies, the authors introduced a distributed and adaptive charging dispatch strategy that uses only local information. It is assumed that all sensors have the same data rate, and the problem lets the charger try to choose a travel path such that the battery of the charger depletes at the fastest rate possible. This decision is made according to the adopted data routing protocol. Furthermore, a partial charging dispatch scheme was devised. The scheme determines the amount of energy to transfer. It was shown to be optimal in terms of the number of active devices. Interestingly, the proposed charging dispatch strategy in [57] was shown by simulation to outperform some strategies based on global information in some cases. 10 Mar 2017 at 08:08:02, .010

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The charging dispatch strategy in [58] was designed on the basis nearest-job-next with preemption discipline. The discipline takes both spatial and temporal characteristics of the incoming charging requests into account. The main idea is to trigger the re-selection of the next to-be-charged node upon either the completion of charging of a device or the arrival of a new charging request. The charger then select the geographically closest requesting node to serve. The authors proposed an analysis to obtain the performance bounds of the throughput and charging delay of the algorithm. Both numerical and system-level simulations were conducted to show that the proposed charging dispatch strategy outperforms the first-come-first-serve discipline. However, the proposed charging dispatch strategy is location-biased. Consequently, it can cause unfairness for wireless power distribution. The authors of [59] developed an online multiple-charger dispatch strategy. The objective is to maximize the charging coverage with on-demand scheduling in an event monitoring wireless-powered sensor network. The authors proved that this problem is NP-complete. To correctly evaluate the network condition, two metrics were introduced. The first metric is called incremental effective coverage (IEC). It is defined in such a way as to represent the set of point of interests [60]. The second metric is called trail covering utility (TCU). It is defined as the average coverage utility during the charging time of the sensor. The authors then introduced three greedy heuristic algorithms that serve to-be-charged devices on the basis of maximum IEC, maximum average TCU, and maximum average TCU with multiple chargers. The first two algorithms were shown to achieve comparable performance in terms of charging coverage. For the third algorithm, the simulation clearly indicated the tradeoff between the charging coverage and the number of chargers deployed.

9.3.3

Discussion and Conclusion Table 9.2 summarizes the aforementioned offline dispatch strategies. The strategies are compared in terms of the number of chargers applied, the energy constraint of the charger(s), optimization variables in the proposed strategies, charging patterns (point-topoint or point-to-multipoint charging), control methods (centralized or distributed), and evaluation methods. Four performance evaluation approaches are typically adopted, i.e., numerical simulation, system-level simulation, theoretical analysis, and experiment. Table 9.2 also highlights that most of the existing work is based on centralized control mobile charger scheduling. Distributed algorithms have been studied and proposed less often, especially for multiple-charger dispatch strategies. Furthermore, all the existing multiple-charger dispatch strategies are based on point-to-point charging, in which landmark selection can be incorporated to further reduce the length of travel tours for multiple chargers. Table 9.3 summarizes the online charging dispatch strategies. The table compares the related work in terms of objectives, number of chargers applied, energy constraint of the charger(s), charging patterns, control methods, and evaluation methods. It is worth noting that reference [59] provides the solution for multiple chargers. Yet, efficient 10 Mar 2017 at 08:08:02, .010

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Table 9.2. Summary of offline mobile charger dispatch strategies: Cen., centralized; Dis, distributed Charger

Optimization Variable

Reference

Number Energy constraint

[27] [30] [24] [25] [31] [32] [33] [42] [41] [40] [29] [28] [45] [44] [47] [48] [54] [50] [49] [52] [53]

Single Single Single Single Single Single Single Single Single Single Single Single Single Single Single Multiple Multiple Multiple Multiple Multiple Multiple

Travel Path     

No No No No No No No No No No No No Yes Yes No No Yes Yes Yes Yes No

      

Charging location

        

  



Charging Charger duration number   

Data routing       

          





   

Data rate

 

Control

Cen. Cen. Dis. Dis. Cen. Cen. Cen. Cen. Cen. Cen. Cen. Cen. Cen. Cen. Cen. Cen. Dis. Cen. Cen. Cen. Cen.

Table 9.3. Summary of online charger dispatch strategies: Cen., centralized; Dis., distributed Charger Reference

Number

Energy constraint

[56]

Single

Yes

[55]

Single

No

[57]

Single

No

[58]

Single

Yes

[59]

Multiple

No

Objective

Charging pattern

Control

Mitigate the limit of TSP-based solutions Maximize charging throughput Balance the tradeoff between information knowledge and achieved performance Increase charging throughput and latency over first-come-first-serve principle Maximize charging coverage

Point-to-point charging Point-to-point charging Point-to-point charging

Cen.

Point-to-point charging

Dis.

Point-to-point charging

Dis.

Cen. Dis.

coordination among chargers is missing. How to coordinate chargers for online strategy, especially with distributed control, is an open problem. Moreover, investigating how to manage multiple charging requests for point-to-multipoint charging can be an important future topic of research. 10 Mar 2017 at 08:08:02, .010

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9.4

309

Hardware Designs for Sensor Nodes with Wireless Energy Harvesting This section introduces the hardware design for sensors nodes with wireless energy harvesting. We review basic design principles for RF-based energy harvesting circuits and coupling-based energy harvesting circuits.

9.4.1

RF-based Energy Harvesting Circuit Design The typical components of an RF powered sensor include a sensory circuit, an antenna module, an impedance matching network, and a rectifier [61]. To provide a better understanding of the communication aspects of an RF-based energy harvesting sensor, this subsection introduces basic knowledge with regard to the circuitry implementations, antenna design, matching network, and rectifier.

9.4.1.1

Circuitry Implementations Various RF energy harvester implementations have been introduced and proposed. The implementations are based on various different technologies such as complementary metal–oxide semiconductor (CMOS) devices. According to a recent survey on RF energy harvester implementation in [2], most of the implementations use CMOS technology. The current CMOS technology can achieve 1 V DC output, with −22 dBm to −14 dBm harvested RF power. Though the CMOS technology allows a lower minimum RF input power, the peak RF-to-DC conversion efficiency is typically lower than that of using Schottky diodes, e.g., HSMS-286 [2]. Greater than 70% efficiency can be obtained when the harvested power is above −10 dBm. For RF energy harvesting at a relatively high power (e.g., 40 dBm/10 W), semiconductor–metal–semiconductor technology can be used. In particular, the authors of [62] showed that an output voltage of 30 V can be achieved at 40 dBm input RF power with a conversion efficiency of 85%. However, if the amount of RF power harvested is low, the conversion efficiency is also relatively low. For instance, it is only 10% when the input power is −10 dBm [63].

9.4.1.2

Antenna Design The antenna of an RF module is for receiving RF signals. A combination of small size and high gain is always the main design goal of antenna technology. For example, the authors of [64] summarized and analyzed a comparative study of several antenna designs for RF energy harvesting. The authors of [65] reported several antenna topologies for RF energy harvesting. The authors of [66] compared existing antenna structures. Antenna array design was also studied for effective RF energy harvesting in [67, 69]. Antenna arrays are effective at increasing the capability for low input power. However, a tradeoff exists between antenna size and performance. For hardware implementations, research efforts have been made concerning narrowband antennas. The narrowband antenna usually covers the frequency range from several MHz to tens of MHz. Typical designs are for a single band [70–73], dual bands [67, 74, 75, 77], or triple bands [75, 79, 80]. Moreover, broadband antenna designs (typically on the order of 1 GHz) have been the focus of some recent work [81–88]. 10 Mar 2017 at 08:08:02, .010

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9.4.1.3

Matching Network A matching network is used to reduce the transmission loss from an antenna to a rectifier circuit. Also, it increases the input voltage of a rectifier circuit [89]. The matching network is typically made with reactive components such as coils and capacitors that are not dissipative [90]. The matching network can achieve the maximum power transfer when the impedance at the antenna output and the impedance of the load are conjugates of each other. This procedure is called impedance matching. Currently, there are three main designs of matching network circuits for RF energy harvesting, i.e., transformer, shunt inductor, and LC network. Reference [90] provides a detailed introduction to these circuits.

9.4.1.4

Rectifier A rectifier is used to convert the input RF signals (AC type) received by the antenna to DC voltage. The major challenge of the rectifier design is to generate a stable, batterylike voltage from very low input RF power. In general, there are three main design approaches for a rectifier, i.e., a diode [91], a bridge of diodes [92], and a voltage rectifier multiplier [93]. A diode is the main component of a rectifier circuit. The rectification performance of the rectifier mainly depends on the saturation current, the junction capacitance, and the conduction resistance of the diode(s) [90]. The circuit of a rectifier, especially a diode, determines the RF-to-DC conversion efficiency. Silicon Schottky barrier diodes are the most commonly used diodes for rectennas, and can provide high stability with a small loss. Typically, a diode with a lower built-in voltage can achieve a higher rectifying efficiency. This is because a larger voltage will result in significantly more harmonic signals due to the non-linear characteristics of the diode. This can significantly decrease the rectifying efficiency [94]. The authors of [95] introduced a model to characterize the RF-to-DC rectification with low input power. The model can be used to derive closedform expressions for the equilibrium voltage and the input resistance of the rectifier. A quasi-static model is further developed to describe the dynamic charging of the capacitor of the rectifier.

9.4.2

Coupling-Based Energy Harvesting Circuit Design The design for a coupling-based energy harvesting circuit is based on the magnetic field intensity function. The intensity of the magnetic field can be characterized as a function of the distance d from the source as follows [96]: INr2 H(d) =  , 2 (r2 + d2 )3

(9.1)

where I represents the current, N represents the number of turns, and r is the radius of the transmit coil. From (9.1), increasing the number of turns and the radius of the transmit coil can amplify the intensity. However, such increases have a certain limit insofar as the number of turns and the coil size need to be optimized by taking into account the transmission 10 Mar 2017 at 08:08:02, .010

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311

frequency and resistances [96]. To capture the energy transferred from the transmit coil optimally, the receive coil should be designed with a low impedance [97]. The mutual inductance between the two coils, the quality factor Q, and the load matching factor have a great impact on the power transfer efficiency of a non-radiative charging system [98]. The mutual inductance of a coil pair indicates how a variation in one coil influences the current induced in the other coil. The mutual inductance of a coil pair is proportional to the geometric mean of the self-inductance of the two coils through a coupling coefficient [99]. The coupling co-efficiency, which reflects the tightness of the coupling, is determined by the alignment and distance, the ratio of diameters, and the shape of the two coils. The quality factor Q is defined as the ratio between the energy stored in the resonator and the energy provided by a generator [100]. A higher value of Q leads to a smaller rate of system energy loss in power transmission. Therefore, in a high-Q power system, the oscillation and resonance decline slowly. The quality factor is affected by the selfinductance, resistance, and intrinsic frequency. They mainly depend on the materials used for fabrication of the device. The load matching factor depends on the separation of the two coils. Since the resonance frequencies of a coil pair change as the gap varies [101], a load matching factor measures the tightness of the matched resonance frequencies. Various methods can be used to adjust the load matching factor in order to maintain resonance frequency matching at varying distances, such as coupling manipulation [102], frequency matching [103], impedance matching [105], and resonator parameter tuning [106].

9.5

Energy Scheduling in Wireless-Powered Sensor Networks Wireless sensor networks have been developed in order to collect environment or subject data and transfer the data to a sink or gateway. In wireless sensor networks, sensors have to be powered by energy from their batteries. The energy is then used to collect, compute, and transmit data among sensors toward the sink and gateway node. Wireless sensor networks can be static or mobile. A static wireless sensor network can be used for environment monitoring applications. A mobile wireless sensor network can be used for healthcare and wearable computing applications. The major challenge of wireless sensor networks is the limited energy supply and storage. Therefore, each sensor node needs to have its battery replaced or charged constantly, which limits the usability and data collection performance of the network. One common solution to overcome this limitation is to deploy energy harvesting devices at the sensor nodes so that the nodes can have an independent energy supply for their operation. In particular, the batteries can be replenished automatically without human effort. Among the existing energy harvesting techniques, wireless energy harvesting and transfer has become a popular technology for powering wireless sensor networks [107, 108]. Using the wireless energy harvesting and transfer technique, wireless sensor nodes can maintain sufficient energy for their operations without interruption. The network lifetime and data collection performance of the network can be greatly improved. Nonetheless, some 10 Mar 2017 at 08:08:02, .010

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issues still exist in wireless energy harvesting and transfer in wireless sensor networks, especially for mobile networks. This is due to the fact that the network may lack fixed energy sources. For example, an energy source for wireless power transfer has to be deployed to the environment or human body. The energy source has to be recharged regularly so that it has sufficient energy to be transferred to other sensor nodes. To optimize the energy harvesting and transfer efficiency, it is important to schedule and manage wireless energy transfer strategies that must also meet the requirements on the energy supply and the data collection requirements of the wireless sensor networks. Therefore, in this section, we review optimization formulations that have been developed or proposed for wireless energy harvesting and transfer scheduling. They have been developed for a wireless-powered sensor network. We mainly classify the related work into the categories of centralized and distributed scheduling. For the centralized approach, there is a centralized controller such as an energy gateway. It is assumed to have global information about the networks, e.g., channel states. As a result, the centralized controller is able to optimize how much wireless energy to transfer, and when. The objective is to maximize the amount of energy received by the sensor nodes. In contrast, for the distributed approach, the sensor nodes can make requests to the energy gateway for energy transfer. The requests can be optimized according to their objectives and constraints. We first present the network architecture and optimization formulations in order to obtain energy scheduling strategies.

9.5.1

Centralized Scheduling In a centralized wireless energy transfer scheduling approach, the wireless-powered sensor networks under consideration are body area networks. The network has an energy gateway that receives energy from a wired or wireless charger when the user moves to the corresponding location. The user mobility is random, and thus the energy replenishment of the energy gateway is intermittent and unpredictable. Energy received is stored in a battery of the energy gateway. At the scheduled times, the energy gateway releases energy from its battery and transfers it to other sensor nodes. The energy scheduling has to take the random channel state, which may depend on the distance from the energy gateway to the sensor nodes, into account. To maximize the energy transfer efficiency, the concept of opportunistic scheduling [109] can be adopted. In particular, when the channel states to many sensor nodes are good, the energy gateway tends to schedule energy transfer in a broadcast fashion so that the total amount of energy received is maximized. To optimize the wireless energy transfer scheduling, we formulate an optimization problem based on a Markov decision process (MDP). The problem is solved to obtain an energy transfer scheduling policy that aims to maximize the weighted sum of energy received by the sensor nodes. The optimal policy is observed to exhibit a threshold behavior.

9.5.1.1

System Model Figure 9.4 shows the system model of wireless-powered sensor networks. The energy gateway receives energy when it visits a fixed charger, which is a random event. The 10 Mar 2017 at 08:08:02, .010

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313

Figure 9.4 System model wireless-powered sensor networks [110].

energy replenishment of the gateway is modeled as a two-state Markov chain. The transition matrix is given by & V=

V0,0 V1,0

V0,1 V1,1

' ,

(9.2)

where 0 and 1 represent the states that the gateway does not receive and is receiving energy from the charger, respectively. Vv,v is the transition probability from energy supply state v to state v . The gateway stores the received energy in its battery with the maximum capacity of E units of energy. The state of the battery is defined by an energy state that takes an integer value from 0 to E. Basically, when the gateway receives energy from a charger, the energy state increases by one unit per time slot. The energy gateway both receives data from and transfers energy to N sensor nodes. When the gateway transfers energy, the energy state decreases by one unit per time slot. Different sensor nodes can receive different amounts of energy from the gateway depending on the channel state, which depends on the distance [111]. The gateway has the ability to obtain the channel states of all sensor nodes, and thus it can decide when to transfer energy depending on the channel states. For sensor node i, the channel is modeled as a Markov chain with the transition matrix given by ⎡ ⎤ C0,0 C0,1 · · · C0,Si ⎢ .. .. ⎥ , .. (9.3) Ci = ⎣ ... . . . ⎦ CSi ,0

CSi ,1

···

CSi ,Si

where Cci ,ci is the probability that the current state is ci and changes to ci , where ci , ci ∈ {0, 1, . . . , Si }, and Si is the highest channel state. We assume that, at channel state ci , the sensor node can receive ci units of energy. Broadcast wireless energy transfer is 10 Mar 2017 at 08:08:02, .010

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Figure 9.5 Wireless-powered body area sensor networks [110].

considered, e.g., transfer of RF energy. Depending on the channel states, all the sensor nodes can receive energy transferred from the gateway. An example of a wireless-powered body area sensor network is shown in Figure 9.5.

9.5.1.2

Optimization Formulation To obtain a wireless energy scheduling policy, we formulate an MDP with the following components: , , P, R.  is the state space. is the action space. P is the transition matrix. R is the reward function. We define the state space as follows:      = (V, E, C)V = {0, 1}, E = {0, 1, . . . , E} ,

(9.4)

where V represents the energy supply state, E represents the energy state, and C is a composite channel state for all the sensor nodes. Here, the channel states are encoded in a composite state denoted by C = C 1 × · · · × Ci × · · · × CN ,

(9.5)

where Ci represents the channel state of sensor node i and × denotes a Cartesian product. Here, there are N sensor nodes in total. The MDP has the action space defined as = {0, 1}, where the action is a ∈ . Here a = 0 indicates that the gateway does not transfer energy, while a = 1 indicates that the gateway transfers energy to the sensor nodes. Next, we provide the derivation for the transition matrix P. First, we consider the energy state of the battery of the gateway. The transition of the energy state can be classified into three cases. 10 Mar 2017 at 08:08:02, .010

Sensor Networks with Wireless Energy Harvesting

1.

315

The energy state increases when the gateway receives energy from the charger, and it does not transfer energy. The transition matrix is expressed as follows: ⎡ ⎤ 0 1 ⎢ ⎥ .. .. ⎢ ⎥ . . (9.6) E+ = ⎢ ⎥. ⎣ 0 1 ⎦ 1

2.

The energy state decreases when the gateway does not receive energy from the charger, and it transfers energy. The transition matrix is given by ⎡ ⎤ 1 ⎢ 1 0 ⎥ ⎢ ⎥ E− = ⎢ (9.7) ⎥. .. .. ⎣ ⎦ . . 1

3.

0

There is no change to the energy state when the gateway receives energy from the charger and it transfers energy, or when the gateway does not receive energy from the charger and it does not transfer energy. The transition matrix for this case is E0 = I,

(9.8)

where I is an identity matrix. For matrices E+ , E− , and E0 , each row corresponds to the energy state e = 0, 1, . . . , E. Next, we incorporate channel state transition and derive the matrix of all the sensor nodes as follows: C = C1 ⊗ · · · ⊗ Ci ⊗ · · · ⊗ CN ,

(9.9)

where ⊗ is the Kronecker product. It is applied because we assume that the channel states of all the sensor nodes change independently. Finally, the transition matrix P(a) of the entire state space  is derived. For the action that the gateway does not transfer energy to the sensor nodes, i.e., a = 0, the transition matrix is given by & ' V0,0 E0 V0,1 E0 P(a = 0) = ⊗ C. (9.10) V1,0 E+ V1,1 E+ In this case, if the energy supply state is v = 0, i.e., the gateway does not receive energy from the charger, then the energy state will not change, so E0 is applied. If the energy supply state is v = 1, i.e., the gateway receives energy from the charger, then the energy state will increase. For the action that the gateway transfers energy to the sensor nodes, i.e., a = 1, the transition matrix is expressed as follows: ' & V0,0 E− V0,1 E− ⊗ C. (9.11) P(a = 1) = V1,0 E0 V1,1 E0 In this case, if the energy supply state is v = 0, then the energy state will decrease. Otherwise, for v = 1, the energy state will not change. 10 Mar 2017 at 08:08:02, .010

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9.5.2

Immediate Reward Function We define the composite state variable of the gateway as ω = (v, e, c1 , . . . , ci , . . . , cN ). v is the energy supply state, e is the energy state, and ci is the channel state of sensor node i. The immediate reward function is defined as follows:  N i=1 wi ci , for a = 1 and e > 0, R(ω, a) = (9.12) 0, otherwise, where wi is the weighting of received energy for sensor node i. The reward is defined as the weighted sum of the energy received by all the sensor nodes if the gateway decides to transfer energy when its battery is not empty.

9.5.3

Optimal Policy The solution of the MDP is an optimal wireless energy scheduling policy. The policy π is a mapping from state ω = (v, e, c1 , . . . , ci , . . . , cN ) ∈  of the gateway to action a ∈ . With a discounted reward MDP, the average reward is discounted by a discount factor γ ∈ (0, 1). The discounted reward of the gateway given wireless energy scheduling policy π and discount factor γ is given by ( T )    γ t−1 Jπ (ω0 ) = lim inf E γ R(ωt |at )ω0 . (9.13) T→∞

t=1

Here, state ωt and action at are functions of time t. ω0 is an initial state. The optimal discounted reward function is expressed as follows: V γ (ω0 ) = sup Jπγ (ω0 ),

(9.14)

π∈

where  is a set of all stationary deterministic policies. The Bellman equation is applied to determine the optimal discounted reward V γ (ω), i.e.,    γ  γ  V (ω) = max R(ω|a) + γ P(ω, ω |a)V (ω ) , (9.15) a∈ (ω)

ω ∈

where P(ω, ω |a) is the transition probability from state ω to ω when action a is taken. This is the element of the matrices P(a = 0) and P(a = 1) given in (9.10) and (9.11), respectively. We can apply standard algorithms, e.g., the value iteration algorithm, to obtain the optimal wireless energy scheduling policy. Then, the optimal discounted reward function is expressed as follows:    γ γ   P(ω, ω |a)Vt (ω ) , Vt+1 (ω) = max R(ω|a) + γ a∈ (ω)

=



 γ max Qt+1 (ω, a) , a∈ (ω)

ω ∈

10 Mar 2017 at 08:08:02, .010

(9.16)

Sensor Networks with Wireless Energy Harvesting

where γ

Qt+1 (ω, a) = R(ω|a) + γ



P(ω, ω |a)Vt (ω ), γ

317

(9.17)

ω ∈

is the state action reward function.

9.5.3.1

Numerical Results Figures 9.6(a), (b), and (c) show the optimal energy transfer policy of the gateway. Figure 9.6(a) shows the action with respect to the energy state of the battery and the channel state of node 1, while the channel states of nodes 2 and 3 are fixed at zero. Clearly, we can observe a threshold structure of the policy. When the energy state is low, the gateway will not transfer energy since the channel states of nodes 2 and 3 are also bad. However, if the gateway has more energy in its battery, it will transfer energy. Similarly, the gateway transfers energy if the channel states of the nodes become better (Figures 9.6(b) and (c)). In this case, the energy state is fixed. In [110], we have theoretically proved that the optimal energy transfer policy is a threshold policy. Figure 9.7 shows the average amount of energy received by sensor nodes, average sensor node throughput, and average packet delay of sensor nodes when the energy supply rate, i.e., the supply of energy from the charger to the gateway, is varied. We observe that, as the sensor nodes receive more energy, the throughput improves and the delay is lower. We also notice an interesting result when the number of sensor nodes increases. In this case, the average amount of energy received and the throughput decrease, and the delay increases. When there are more sensor nodes, the gateway has less opportunity to transfer energy when the channel states of all the sensor nodes are good, and thus the performance drops. Then we vary the weighting of the sensor node. From Figure 9.8, we observe that, when the weighting of sensor node 1 increases, the gateway will give priority to transferring energy to this sensor node. For example, the gateway may decide to transfer energy even though the channel quality of sensor node 1 is not the best. As a result, the sensor node receives more energy, and hence the throughput increases, and the delay decreases. This is at the cost of a deterioration in performance of the other sensor nodes. Therefore, in order to meet the performance requirements of different sensor nodes in the network, the weightings of wireless energy transfer scheduling must be chosen appropriately.

9.5.4

Decentralized Scheduling Next, we consider distributed wireless energy scheduling for a wireless-powered sensor network [112]. Again, there is an energy gateway supplying energy to sensor nodes. However, in this case, the sensor nodes send requests for energy transfer when their auxiliary energy supply cannot provide sufficient energy to meet the data transmission requirement. To obtain the distributed wireless energy scheduling policy for the sensor nodes, i.e., the means to request for energy transfer, we introduce a constrained stochastic game model whose objective is to minimize the number of requests, while 10 Mar 2017 at 08:08:02, .010

Xiao Lu

(a)

Transfer action

Policy (energy state)

1

0 10

9 8

7

6

5

3 2 1 0 Channel state of node 1 Policy (channel state) at energy state = 5 4

3

2 1 0 Energy state

Transfer action

(b)

1

3

0

2

3

1

2

0

1

Channel state of node 2 0 Channel state of node 1 (c) Policy (channel state) at energy state = 2

Transfer action

318

1

3

0 3

2 2

1 1

0 Channel state of node 1

0 Channel state of node 3

Figure 9.6 An optimal energy transfer policy with respect to (a) the energy state, (b) channel

states of nodes 1 and 2, and (c) channel states of nodes 1 and 3 [110].

meeting the QoS requirement. The QoS requirement is defined in terms of the maximum energy outage probability. A constrained Nash equilibrium is adopted as a solution. The equilibrium ensures that the policies of all sensor nodes will not violate the QoS requirement and will minimize the cost of satisfying a request for energy.

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Node throughput

Average energy received

Sensor Networks with Wireless Energy Harvesting

1 0.8 1 node 2 nodes 3 nodes

0.6 0.4 0.2

0.3

0.4

0.5 Energy supply rate

0.6

0.7

0.8

0.3

0.4

0.5 Energy supply rate

0.6

0.7

0.8

0.3

0.4

0.5 Energy supply rate

0.6

0.7

0.8

0.3 0.25 0.2 0.15 0.1 0.2

Average packet delay of nodes

319

150

100

50 0.2

Figure 9.7 The average amount of energy received, average sensor node throughput, and average

packet delay of sensor nodes versus energy supply rate.

We introduce an iterative algorithm based on best response dynamics to obtain the equilibrium.

9.5.4.1

System Model The wireless-powered sensor network under consideration is composed of a wireless energy gateway and sensor nodes as shown in Figure 9.9. The wireless energy gateway supplies wireless energy when at least one sensor node requests it. With broadcast wireless energy transfer, e.g., using RF energy transfer technology, multiple sensor nodes can receive energy simultaneously. The amount of energy received depends on the channel state from the wireless energy gateway to the sensor node [111]. The channel state is also random, and the state takes a value from the set C = {0, 1, . . . , C}, where C is the highest channel state. When the wireless energy gateway transfers wireless

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0.38 Node 1 Node 2 Node 3

Node throughput

0.36 0.34 0.32 0.3 0.28 0.26

2

4

6

8

10

12

14

10

12

14

Weight of node 1 Average packet delay of nodes

320

70 65 60 55 50

2

4

6

8 Weight of node 1

Figure 9.8 Sensor node throughput and average packet delay of sensor nodes versus the

weighting of sensor node 1.

energy, at state c ∈ C, the sensor node can receive c units of energy. The channel state is modeled as a Markov chain with the transition matrix for node n denoted as follows: ⎡

C0,0 ⎢ .. Cn = ⎣ .

C0,1 .. .

CC,0

CC,1

··· .. . ···

⎤ C0,C .. ⎥ , . ⎦

(9.18)

CC,C

where Cc,c is the probability that the channel state is c, and it changes to c . In addition to the energy supply from the wireless energy gateway, the sensor nodes can have auxiliary energy sources, e.g., from vibration-based energy harvesting [113]. The amount of energy derived from the auxiliary energy sources is, however, random and might not be sufficient to support the operation of the sensor nodes. The set of auxiliary energy sources of sensor node n is denoted by Sn . Similarly to the channel state, the energy receiving state of auxiliary energy source s ∈ Sn is denoted by x ∈ {0, 1, . . . , Hs }, where Hs is the highest state. The sensor node can receive x units of 10 Mar 2017 at 08:08:02, .010

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Figure 9.9 System model of a wireless-powered body area network [112].

energy at state x. The transition matrix of auxiliary energy source s is then expressed as follows: ⎡ ⎤ X0,0 X0,1 · · · X0,Hs ⎢ ⎥ .. .. .. (9.19) Xn,s = ⎣ ... ⎦, . . . XHs ,0

XHs ,1

···

XHs ,Hs

where again Xx,x is the probability that the energy receiving state is x, and it changes to x . Energy received from the wireless energy gateway and auxiliary sources is stored in the battery of the sensor node. We assume that the energy state of the battery is divided into finite discrete levels, referred to as units of energy. The maximum capacity of the battery of sensor node n is Bn units of energy. The sensor node generates data to be transmitted to the gateway randomly with probability αn . The data must be transmitted immediately after their generation, i.e., the process is delay sensitive. The data transmission consumes Kn units of energy from the battery. If there is not enough energy in the battery, the data cannot be transmitted, and will be dropped. This is called an energy outage event, and the frequency of occurrence of such events needs to be maintained below a certain threshold. Given the aforementioned system description, the sensor nodes must decide rationally and independently whether to request wireless energy transfer or not. Sending the request incurs a cost Mn for sensor node n. Thus, the sensor node aims to minimize the number of requests sent out, given the energy in its battery and energy supplied by the auxiliary energy sources. Moreover, the energy outage probability must be kept below a threshold On . Distributed wireless energy transfer scheduling will be proposed as a means for helping the sensor nodes make such a decision without explicit information exchange, minimizing the signaling overhead. 10 Mar 2017 at 08:08:02, .010

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9.5.4.2

Optimization Formulation To obtain the distributed energy transfer scheduling/request policy, we formulate a constrained stochastic game model [114]. In the game model, there are N players, i.e., sensor nodes. Let N denote a set of players. Each player is characterized by the tuple {n , An , Pn , Cn , Vn }. They are defined as follows. •

•

• • •

n is a finite local state space of sensor node n, in which ωn ∈ n denotes / / is the Cartesian a local state.  = N n=1 n/is a global state space, where product. Moreover, −n = n =n n denotes the state space of all the sensor nodes except sensor node n. / An is a finite local action space. A = N n An is a global action space. a = (a1 , . . . , an , . . . , aN ) ∈ A denotes the global action. Again, the actions of all sensor nodes except sensor node n is defined by a−n = (a1 , . . . , an−1 , an+1 , . . . , aN ) / ∈ A−n = n =n An . Pn (a) is a transition probability matrix for sensor node n taking action a. Cn is an immediate cost function. Vn = {Vn,j } is a set of constraints.

In the following, we define each of the above game components. First, the local state space of sensor node n is given as follows:   (9.20) n = (En , Cn , Xn ) . • • •

En = {0, 1, . . . , Bn } is the energy state of the battery. Cn ∈ C is the channel state. Xn is the composite energy receiving state of the auxiliary energy sources. This composite energy receiving state is defined as Xn = (Xn,1 , . . . , Xn,s , . . . , Xn,Sn ),

(9.21)

where Xn,s is the energy receiving state of auxiliary energy source s of sensor node n. The composite state variable of the node is denoted by ωn = (e, c, x1 , . . . , xs , . . . , xSn ) ∈ n . An = {0, 1} denotes the action space, where An = 0 if the sensor node does not send an energy request to the wireless energy gateway, and An = 1 if the sensor node sends a request. Given the state space, the state transition is derived for sensor node n. The transition matrix of an energy state when there are i units of energy arriving, i.e., from the wireless energy gateway or auxiliary sources, is denoted by Ei . Ei has an element denoted by (i) Ee,e , which is the probability that the energy state changes from e to e . The probability can be obtained as follows. •

For e + i ≥ Kn , the sum of the energy arriving and the current energy in the battery is greater than or equal to the energy consumption for data transmission. (i) The probability is Ee,e = αn for e = min(Bn , e + i − Kn ), which is the case that the sensor node generates data to be transmitted. Alternatively, the probability is 10 Mar 2017 at 08:08:02, .010

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Ee,e = 1 − αn for e = min(Bn , e + i), which is for the case in which the sensor node does not generate data to be transmitted. The energy state cannot exceed the maximum capacity of the battery, and thus it is limited by the expression min(Bn , ·). For e+i < Kn , the sum of the energy arriving and the current energy in the battery is not sufficient to support data transmission, and thus an energy outage event occurs. Since there is no data transmission, the energy will not be consumed. The (i) probability is Ee,e = 1 for e = min(Bn , e + i). (i)

•

Next, the channel state and energy receiving states are incorporated with the energy state. The transition matrix is expressed as follows: Yn = Cn ⊗ Xn,1 ⊗ · · · ⊗ Xn,s ⊗ Xn,Sn .

(9.22)

Each row of the matrix Yn represents the probability corresponding to the channel state c and energy receiving states (c, x1 , . . . , xs , . . . , xSn ). Again, here xs is the amount of (n) energy received from auxiliary energy source s. The matrix Yn has elements Yy,y . y =   (c, x1 , . . . , xs , . . . , xSn ) and y = (c , x1 , . . . , xs , . . . , xSn ) are the current and next channel state and energy receiving states, respectively. Then the transition matrix of each sensor node n is obtained for action a as follows. •

an = 0. Energy arriving is only from the wireless energy gateway when one of sensor nodes sends an energy request. The transition probability denoted by (n) Py,y (a) is obtained as follows:  (n) Py,y (a)

•

=

(n) Yy=(c,x1 ,...,xs ,...,xS ),y n

λ−n EI+c + (1 − λ−n )EI , an = 0, an = 1, EI+c ,

(9.23)

n where I = Ss=1 xs is the number of units of energy received from all auxiliary energy sources given energy receiving states xs . In this case, when the sensor node decides not to request wireless energy transfer (i.e., an = 0), the energy state transition EI+c is applied only if one of the other sensor nodes does request wireless energy transfer. The probability that the other sensor nodes request wireless energy transfer is denoted by λ−n . If none of the sensor nodes requests energy, there is only energy supply to sensor node n from the auxiliary energy sources, and thus the transition matrix EI is applied. an = 1. Energy can be supplied from the wireless energy gateway. The energy supply will be I + c units, which corresponds to the energy state transition EI+c .

The immediate cost of the sensor node n, i.e., Cn (ωn , an ), is defined as the state ωn = (e, c, x1 , . . . , xSn ) as follows:  Cn (ωn , an ) =

Mn , an = 1, 0, otherwise.

10 Mar 2017 at 08:08:02, .010

(9.24)

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That is, requesting wireless energy transfer incurs cost Mn . The immediate energy outage probability, which is the QoS constraint of the sensor node, is given by ⎧ n ⎪ (1 − λ−n )αn , for an = 0 and e + Ss=1 x < Kn , ⎪ ⎪  sn ⎨ for an = 0 and e + c + Ss=1 x < Kn , λ−n αn , (9.25) Vn (ωn , an ) = Sn s ⎪ for an = 1 and e + c + s=1 xs < Kn , αn , ⎪ ⎪ ⎩ 0, otherwise. Kn is the number of units of energy required to transmit data by the sensor node. •

•

•

The first condition of (9.25) is when the sensor node does not request energy and neither do other sensor nodes, and the sum of the energy arriving and the current energy of the battery is less than that needed for data transmission. The second condition of (9.25) is when the sensor node does not request energy, but one of the other sensor nodes does. However, still the sensor node does not have enough energy to transmit data. The third condition of (9.25) is when the sensor node requests wireless energy transfer.

We aim to obtain a local stationary policy πn of the sensor node. Here, the policy is the probability that sensor node n takes local action an when the local state is ωn . The stationary multi-policy π consists of the stationary policies of all sensor nodes, meaning that it is basically a combination of the policies of all sensor nodes. Then, π−n denotes the stationary policies of all sensor nodes except sensor node n. The objective of the sensor node is to minimize the average cost defined as follows: T  1  Eπ Cn (ωt , at ) , T→∞ T

Cn (π ) = lim

(9.26)

t=1

where ωt is the global state and at is the global action at time t. The constraint on the energy outage probability is expressed as follows: T  1  Eπ Vn (ωt , at ) ≤ On , T→∞ T

Vn (π ) = lim

(9.27)

t=1

where On is the energy outage probability requirement of sensor node n. The solution is a constrained Nash equilibrium defined as the multi-policy π ∗ = ∗ ) that meets the following condition: (πn∗ , π−n     ∗ ∗ ) ≤ Cn (πn , π−n ) . (9.28) Cn (πn∗ , π−n ∗ ) is feaThis is for all sensor nodes n = 1, . . . , N among any πn such that (πn , π−n sible (i.e., the constraint is met). The constrained Nash equilibrium is the solution that the sensor node cannot achieve a lower cost by changing its stationary policy πn while the other sensor nodes do not alter their stationary policies. Notably, the constrained Nash equilibrium must not violate the constraint on the energy outage probability requirement.

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We adopt the best-response policy πn∗ of sensor node n given the policies of other sensor nodes π−n to obtain the constrained Nash equilibrium. The best-response policy is given by     (9.29) Cn (πn∗ , π−n ) ≤ Cn (πn , π−n ) . The best-response policy can be obtained by solving the corresponding linear programming (LP) problem for sensor node n. φn,π−n (ωn , an ) denotes the stationary probability of taking local action an at local state ωn given stationary policies of other sensor nodes ∗ (ωn , an ), π−n . We solve the following LP to obtain φn,π −n min





φn,π−n (ωn , an )Cn (ωn , an )

ωn ∈n an ∈An

subject to





φn,π−n (ωn , an )Vn (ωn , an ) ≤ On ,

ωn ∈n an ∈An





φn,π−n (ωn , an )Pωn ,ωn (an )

ωn ∈n an ∈An



= 

φn,π−n (ωn , an ), ωn ∈ n ,

an ∈An



φn,π−n (ωn , an ) = 1,

ωn ∈n an ∈An

φn,π−n (ωn , an ) ≥ 0,

(9.30)

where Pωn ,ωn (an ) is obtained as in (9.23). Supposing that the LP is feasible, the stationary best-response policy of sensor node n is computed from πn∗ (ωn , an ) = 

∗ φn,π (ωn , an ) −n an ∈An

∗ φn,π (ωn , an ) −n

, for ωn ∈ n .

(9.31)

To obtain the constrained Nash equilibrium, the best-response dynamics is applied for every sensor node to adjust its policy. Notably, the policy of any sensor node affects the policies of other sensor nodes due to the parameter λ−n , i.e., the probability that sensor nodes request wireless energy transfer. To obtain this probability, we first derive the probability that individual sensor node n requests wireless energy transfer, i.e.,  φn,π−n (ωn , an = 1). (9.32) λn = ωn ∈n

Then, λ−n is given by λ−n = 1 −

(1 − λn ).

(9.33)

n =n

For the implementation of the best-response dynamics, Algorithm 9.1 shows the major steps. 10 Mar 2017 at 08:08:02, .010

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Algorithm 9.1 Best response dynamics Initialize the stationary policy πn for all sensor nodes. repeat for All sensor nodes n do Calculate probability λ−n ∗ Sensor node n solves LP in (9.30) to obtain φn,π (ωn , an ) and πn∗ (ωn , an ). −n end for until Stationary policies of all sensor nodes converge.

9.5.4.3

Numerical Results We evaluate the convergence of the best-response dynamics algorithm as shown in Figures 9.10(a) and (b). Here, there are three sensor nodes, and, while the stationary policy of sensor node 3 is fixed, those of sensor nodes 1 and 2 are varied. Figure 9.10(a) shows the adaptation of the average wireless energy request rates. The wireless energy request rates of sensor nodes 1 and 2 converge to the constrained Nash equilibrium point. Then, Figure 9.10(b) shows the policy adaptation over time. We observe that the best-response dynamics algorithm can converge to the constrained Nash equilibrium quickly, i.e., within a few iterations. We show the stationary policies at the constrained Nash equilibrium in Figures 9.11(a), (b), and (c) for sensor nodes 1, 2, and 3, respectively. The policies are plotted against the energy and channel states. Clearly, the sensor node will request wireless energy transfer when its energy state is low and the channel state is good so as to maximize the opportunity of receiving a large amount of energy when it is needed for data transmission. We next evaluate the impact of the energy supply from an auxiliary energy source. Figure 9.12 shows the wireless energy request rates of all the sensors under equilibrium policies. We vary the arrival rate of energy from the auxiliary energy source of sensor 2, while the rates of sensors 1 and 3 are fixed at 0.1. Clearly, sensor 2 requests wireless energy less frequently. However, this reduces the wireless energy supply to sensors 1 and 3, and hence they have to request energy more frequently, incurring a higher cost to them. Furthermore, Figure 9.12 shows the simulation results, which match well with the analytical results. This helps verify the accuracy of the proposed analytical game models and equilibrium policies.

9.6

Future Research Directions For wireless-powered sensor networks, the following issues merit further study. •

Joint energy transfer and data transmission scheduling. Data transmission can share the same spectrum as energy transfer, e.g., RF energy. Thus, the energy transfer and data transmission of a sensor node have to be jointly optimized to efficiently utilize energy and radio resources. Joint energy transfer and data transmission scheduling will take the channel state into account. 10 Mar 2017 at 08:08:02, .010

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Average wireless energy request rate of node 2

(a)

0.16

0.14

0.12

0.1

0.08

Best response of node 1 Best response of node 2 Equilibrium

0.06

0.04

(b)

0.02

0.04 0.06 0.08 0.1 Average wireless energy request rate of node 1

0.12

0.14

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0.2

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0.05

Node 1 Node 2 Node 3

0 0

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7

Iteration Figure 9.10 (a) Attraction and (b) convergence to an equilibrium policy [112].

•

Localization for RF-based energy beamforming. Owing to the attenuation of wireless power over an air gap, the transmission efficiency is usually low. Energy beamforming is helpful to enhance the power transmission efficiency. However, the energy transmitter needs to know the location of the energy receiver to which it must steer the energy beam. Localization needs to make real-time spatial estimations for two major parameters, i.e., angle and distance. Self-detection and localization of to-be-charger devices is challenging, especially for mobile 10 Mar 2017 at 08:08:02, .010

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(b) Probability of requesting wireless energy

1 0.5 0 20

19

18 17

16

15

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4

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(c) Probability of requesting wireless energy

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(a)

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Figure 9.11 Equilibrium policies of (a) sensor 1, (b) sensor 2, and (c) sensor 3 with energy consumption, i.e., data transmission, probabilities of 0.18, 0.20, and 0.22, respectively [112].

Figure 9.12 Sensor wireless energy request rate versus auxiliary energy arrival/harvesting rate. 10 Mar 2017 at 08:08:02, .010

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•

•

•

9.7

329

wireless-powered communication networks. Additionally, channel estimation is also very critical in the design of beamforming vectors. Relay for wireless power transfer. Low wireless power transfer efficiency is still a fundamental bottleneck that limits the wide adoption of wireless charging. To extend the coverage range, the concept of multi-hop RF energy transfer (e.g., [115] for RF-based and [116] for coupling-based wireless charging) has been proposed to improve the energy transfer efficiency by deploying relay nodes to harvest and broadcast energy. In this approach, the overall charging efficiency is greatly influenced by the number and placement of relay nodes as well as the number of hops required. Optimization is needed to determine these three decision variables, with the objective being to maximize the charging efficiency. Energy provisioning for mobile sensors. Mobile energy provisioning is challenging for mobile wireless-powered sensor nodes. The major issue is due to the fact that the charging efficiency and data transmission performances are timevarying in mobile environments. Thus, energy provisioning has to be dynamic and adaptive. The main problems to be solved include (i) how to keep track of a mobile device with wireless energy harvesting and (ii) how to efficiently deliver wireless power when a line-of-sight link is not available. Wireless-powered Internet of Things (IoT). The IoT has emerged as a new paradigm that embraces sensor networks as data sources. The IoT will connect a number of Internet devices using machine-to-machine (M2M) communication via the cloud. Wireless energy transfer that takes the energy consumption of sensors and an M2M gateway can be developed to support various IoT applications.

Summary This chapter first presents the important aspects of wireless-powered sensor networks. Two important research problems of wireless energy transfer in sensor networks, i.e., static charger deployment and mobile charger dispatch, are discussed and a number of related works are reviewed. Then, we propose a form of wireless energy transfer scheduling that allows an energy source to efficiently transfer energy to sensor nodes, taking channel states into account. The centralized approach formulates a Markov decision process in order to obtain an optimal energy transfer scheduling policy. Alternatively, the distributed approach formulates a constrained stochastic game in order to obtain a constrained Nash equilibrium energy request policy. Finally, we discuss some important future research directions in wireless-powered sensor networks.

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10

Cognitive Radio Networks with Wireless Energy Harvesting Dinh Thai Hoang

10.1

Introduction A cognitive radio network (CRN) is an intelligent radio network in which unlicensed users (i.e., secondary users) can opportunistically access idle channels when such channels are not occupied by licensed channels (i.e., primary users). The main purpose of CRNs is to utilize available spectrum efficiently, since spectrum is becoming more and more scarce due to the boom in wireless communication systems. Basically, we can define a cognitive radio as a radio that can change its transmitter parameters as a result of interaction with the environment in which it operates [1]. From this definition, there are two main characteristics of cognitive radio that are different from traditional communication systems, namely cognitive capability and reconifigurability [2]. • •

Cognitive capability. This characteristic enables cognitive users to obtain necessary information from their environment. Reconfigurability. After gathering information from the environment, the cognitive users can dynamically adjust their operating mode to environment variations in order to achieve optimal performance.

To support these characteristics of cognitive radio, there are four main functions that need to be implemented for cognitive users. •

• • •

Spectrum sensing. The goal of spectrum sensing is to determine the channel status and the activity of the licensed users by periodically sensing the target frequency band. Spectrum analysis. The information obtained from spectrum sensing is used to schedule and plan for spectrum access. Spectrum access. After a decision has been made on the basis of spectrum analysis, unlicensed users will be allocated access to the spectrum holes. Spectrum mobility. Spectrum mobility is a function related to the change of operating frequency band of cognitive users. The spectrum change must ensure that data transmission by cognitive users can continue in the new spectrum band.

Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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Under these functions, cognitive users can utilize the limited spectrum resource in a more efficient and flexible way. Recently, the development of wireless power transfer technologies has brought a new research direction, called wireless-powered cognitive radio networks (CRNs), which would seem to provide a promising solution for energy conservation for CRNs. In wireless-powered CRNs, secondary users are able to harvest energy wirelessly and then use the harvested energy to transmit data to the primary channels opportunistically. There has been much research investigating different applications of different forms of energy harvesting techniques for CRNs. For example, a framework that involves exploiting energy from polarization for CRNs was proposed in [3]. In particular, in this framework, secondary users are equipped with a solar-powered energy harvesting functionality with the aim of enhancing the efficiency of cooperation in CRNs and avoiding interference between the secondary and primary networks. Then, in order to maximize the average throughput for the secondary system, the authors adopted a Markov decision process (MDP) framework together with the dynamic programming technique. By exploiting polarization in CRNs, it is expected that the bottleneck in the evolution of wireless communications can be overcome. Another form of wireless energy that has received a lot of attention in the literature is ambient wireless energy harvesting. For example, the authors of [4–6] studied the harvesting of energy from ambient sources, e.g., heat, solar, and vibration, for secondary systems. Specifically, the authors of [4] introduced a scenario in which the secondary user can exploit energy from the surrounding environment, and then use such harvested energy to transmit data to the primary channel when this channel is not occupied by primary users. The energy arriving in the energy queue at each time slot is assumed to be independent. Depending on the current amount of energy harvested, the secondary user has to choose to go to sleep mode or perform spectrum sensing to detect primary signals with the goal of maximizing its throughput. Then, an offline method based on an MDP framework was also adopted to determine the optimal mode for the secondary user. Similarly to [4], the authors of [5, 6] also studied optimal policies for unlicensed systems in wireless-powered CRNs. However, differently from [4], in [5], an online energy allocation policy was adopted to decide whether a system should remain idle or perform sensing. The authors of [6] studied performance analysis to determine optimal spectrum sensor detection thresholds for secondary users. Through simulation results, all of these authors showed the efficiency of using energy as well as spectrum in CRNs with energy harvesting. Recently, with the development of far-field wireless energy harvesting techniques, radio-frequency (RF) energy harvesting has been introduced and promptly received a lot of attention regarding its use in wireless networks, especially in CRNs, owing to its many advantages. • •

Pervasive environment. RF sources are available almost everywhere, providing an abundant energy resource for wireless nodes. Long distance and multiple directions. Owing to the electromagnetic radiation feature of radio signals, RF energy techniques enable energy to be not only

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•

transfered to a distant destination (up to a few kilometers away), but also broadcast in all directions, which allows multiple charging simultaneously. Power control. From the Friis equation in Chapter 1, it can be seen that the amount of energy harvested can be controlled by adjusting the transmission power at the RF sources.

Because of the advantages of using RF energy harvesting in CRNs, there has been much research focusing on this topic. In [7], an RF-powered CRN for body area networks was studied. In particular, physiological information about a patient obtained via sensors is gathered and sent to the hospital through cognitive channels when these channels are not occupied by primary users. Sensors are assumed to be powered by RF energy scavenging and then they use this energy to access the channels opportunistically. Alternatively, the authors discussed challenges in designing and implementing the physical, MAC, and network layers and introduced some potential solutions. Finally, a practical scenario was examined to evaluate for the proposed model, e.g., how to utilize the harvested RF to power sensor nodes. From the results obtained, the authors concluded that RF energy harvesting has a promising future for power supply in wireless body area networks. In [8], a secondary user (SU) is equipped with a finite energy buffer to harvest energy from primary signals when it is close enough to primary transmitters. In addition, the SU can transmit data to its destination when it is sufficiently far away from primary transmitters. On the basis of these assumptions the authors proposed a stochasticgeometry model of the CRN where primary users (PUs) and SUs are distributed as independent homogeneous Poisson point processes (HPPPs) [9]. In this model, PUs are protected from interference from the SUs by a guard zone, and transfer a significant amount of RF energy to an SU when they lie within a harvesting zone. Employing the stochastic-geometry model, the authors adopted the Markov-chain theory to derive the transmission probability of the SU and then used a Poisson approximation of the transmitting SU to derive the maximum throughput for the SU. An important result found in this paper is that the maximum throughput of the SU increases linearly with increasing density of PUs. Furthermore, the density of PUs is inversely proportional to the transmission probability of the SU. The authors of [10] studied an application of the RF energy harvesting technique in a cognitive amplify-and-forward relaying network. In particular, there is a CRN with one primary user and three secondary users (SUs), called a source SU (SS), a relay SU (RS), and a destination SU (DS), as illustrated in Figure 10.1. The RS forwards the information received from the SS to the DS by using the energy harvested from RF signals of the source SU (i.e., the SS) in order to optimize the network performance within N time slots. At each time slot, the SUs first perform sensing to detect the operation of primary users. If the primary channel is occupied by primary users, the SUs use the IDLE mode. Otherwise, data will be transmitted to the channel through two phases, i.e., from SS to RS and from RS to DS (each phase lasts for half of a time slot). Given the proposed system, the authors formulated the throughput maximization problem and then adopted an approximation method using the upper bound to mitigate the complexity of the optimization problem. In addition, a suboptimal algorithm was developed in order Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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Figure 10.1 Relay-assisted cognitive radio networks.

to achieve near-optimal throughput performance. The results demonstrated that, with the proposed approximation algorithm, the average throughput obtained is close to the optimal solution and there is a significant gain compared with the separate management algorithm. The authors of [11] considered a scenario in which there are two primary users, denoted by S and D, who want to exchange information, but the distance between them is too great and thus they cannot communicate directly with each other. However, there is a secondary user R who volunteers to relay signals for primary users S and D. At the same time, the secondary relay node R also has its own information and wants to transmit to the secondary user C as illustrated in Figure 10.2. Consequently, the node R has to transmit primary relay information and its own information simultaneously. Differently from the scenario considered in [10], in [11], it is assumed that, when the relay node R receives signals from primary nodes, it is able to extract information and energy from RF signals. Then, by using the energy harvested from RF signals, the relay node can transmit information to primary and secondary nodes. For the proposed aforementioned network, the authors formulated outage probability expressions for the primary nodes and derived lower/upper bounds of the outage probability for the secondary nodes. From analysis results, it was demonstrated that the proposed protocol has better outage performance than direct transmission without spectrum sharing. In [12], an RF energy harvesting technique for cellular cognitive device-to-device (D2D) networks was studied. In such networks, D2D transmitters are able to harvest RF energy from ambient interference caused by transmissions of macro base stations and cellular users, and then perform sensing to transmit data to a predefined non-exclusive D2D channel. To deal with the multi-channel system and the coexistence of cellular and D2D users, the authors introduced two methods to access the channel. Under these Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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Figure 10.2 Two-way cognitive relay network.

channel access policies, a packet is successfully transmitted from a D2D transmitter to its receiver if the D2D channel is idle and the signal-to-interference-plus-noise ratio (SINR) at the D2D receiver is under the predefined threshold. In order to analyze the performance of the proposed network, tools from stochastic geometry were adopted. One of the most important findings in this paper is that, for the proposed system with a low density of base stations, downlink channels have a better performance than that of uplink channels. However, in an environment with a high density of base stations, uplink channels are preferable for D2D transmissions. The authors of [13] studied an optimal mode selection policy for a secondary user in an RF-powered CRN. It was assumed that there is a primary user and that the SU can harvest energy when the PU transmits data or transmit data when the PU is idle. However, the SU cannot harvest RF energy and access the primary channel simultaneously, thus it has to opt for either access mode or harvest mode at the beginning of each time slot. Alternatively, it is assumed that the SU does not have any information about the current state of the channel in advance, but it knows a part of the channel state (e.g., the idle channel probability). Therefore, the partially observable MDP (POMDP) framework was adopted to obtain the optimal mode selection policy for the SU. While in [13] the POMDP framework was used to determine whether to transmit data or harvest energy, in [14] the authors adopted a POMDP framework to find the optimal sensing policy for the SU, i.e., go to sleep mode or perform sensing. In addition, to maximize the average expected throughput, the authors transformed the constrained POMDP to an unconstrained POMDP and proposed an approximate method to reduce the computational complexity. From their numerical results, the authors concluded that, by exploiting the temporal correlation of the primary traffic, the proposed approach Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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can achieve efficient usage of harvested energy. However, both in [13] and in [14], the throughput optimization problem in RF-powered CRNs was considered with only one SU and PU. For more than one PU, the channel selection problem must be taken into consideration, as shown in some papers [15–17]. This is a common problem that we have to face in wireless-powered CRNs in practice when SUs need to find the best channels to maximize their throughput. Therefore, in this chapter, we will discuss this problem together with solutions regarding how to find optimal policies for SUs. The rest of this chapter is organized as follows. First, we present an opportunistic channel access and RF energy harvesting model for SUs. Then, we discuss the case when SUs are interested in maximizing their overall throughput. Finally, we investigate a scenario with the appearance of jammers in such an environment.

10.2

Opportunistic Channel Access for RF-powered Cognitive Radio Networks We consider a CRN that consists of one secondary user (SU) and C non-overlapping primary channels as illustrated in Figure 10.3. Time is assumed to be slotted, and at each time slot any particular primary channel can only be either idle or busy. If the channel is not occupied by primary users (PUs), i.e., the channel is busy, the SU can transmit data, whereas if the channel is not occupied by PUs, i.e., the channel is idle, the SU will perform harvesting of RF energy from PUs’ signals. We denote by phar c the probability that the SU can harvest successfully one unit of RF energy on channel c. If a unit of energy is harvested successfully, it will be stored in an energy buffer. We assume that the SU is equipped with a data buffer and an energy storage device that have maximum queue sizes of Q packets and E units, respectively. We denote the probability that a new packet arrives in the SU’s data queue by λ, and it is assumed that the SU uses etran su units of energy to transmit a packet from the data queue to an idle channel and the probability that this packet is transmitted successfully to the receiver over the channel c is ptran su . When the SU senses the primary channels to detect PU signals, the sensing process may have wrong results, e.g., because of noise or a hardware mistake. If the current channel is busy, but the SU’s sensing result is idle, it is called miss detection,

Figure 10.3 System model for the opportunistic channel access problem of a secondary user in RF energy harvesting CRNs.

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and we denote the miss detection probability for channel c by pmiss c . On the other hand, the probability that the SU’s sensing result is busy, but the current channel is idle, is . denoted by pfalse c Since at each time slot the channel status is either idle or busy, we will use a two-state Markov chain to model for a given channel state c as follows: & Cc =

C0,0 (c) C0,1 (c) C1,0 (c) C1,1 (c)

'

← idle ← busy,

(10.1)

where “0” and “1” correspond to the case when the channel is idle and busy, respectively. From (10.1), we can derive the idle channel probability for channel c as follows: pidle c = (1 − C1,1 (c))/(C0,1 (c) − C1,1 (c) + 1). Depending on the observed information, there are three cases then can affect to the decisions of the SU. •

•

•

10.2.1

In the first case, we assume that the secondary user has a full set of model parameters, e.g., probabilities of successful packet transmission and RF energy harvesting, and the probability of the channel being idle. In addition, it is also assumed that the secondary user knows the current status of all the channels. Therefore, an optimization problem is formulated to find the optimal channel access policy for the secondary user. This scenario might not be true in practice, but it can be used for benchmarking with our proposed solution. The details of this optimization formulation can be found in [18]. In the second case, we assume that the secondary user has some information about the environment, which we refer to as the model parameters. Nevertheless, the secondary user does not know the current channel status (i.e., whether it is idle or busy) before it senses the channels. An optimization formulation based on an MDP will be studied to find the optimal channel access policy. The detail of this optimization formulation is presented in Section 10.2.1. Finally, in the last case, we assume that the secondary user has no information about the environment, i.e., model parameters, and thus it must observe the environment and select the channel to access according to its own information. We will study an online learning algorithm to obtain the channel access policy for the secondary user. This case will be discussed in Section 10.2.2.

Markov Decision Process Framework In this section, an MDP is adopted to formulate the channel access problem for the secondary user and to obtain the performance measures.

10.2.1.1

State Space and Action Space We define the state space of the secondary user as follows:   S = s = (e, q); e ∈ {0, 1, . . . , E}, q ∈ {0, 1, . . . , Q} ,

(10.2)

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where s = (e, q) ∈ S is the state of the secondary user, which is determined by the energy queue state e and data queue state q. Depending on the current state of the secondary user, we need to find an appropriate channel in order to harvest energy or transmit data such that the average throughput of the secondary user is maximized. Thus, the action a for the secondary user is choosing a channel c from the set of {1, . . . , C} to sense. Then, we can define the action space by A = {1, . . . , C}.

10.2.1.2

Transition Probability Matrix Given an action a ∈ A, we can derive the transition probability matrix for the secondary user as follows: ⎤ ⎡ ←q=0 B0,0 (a) B0,1 (a) ⎥ ←q=1 ⎢ B1,0 (a) B1,1 (a) B1,2 (a) ⎥ ⎢ P(a) = ⎢ (10.3) ⎥ . .. .. .. ⎣ . . . ⎦ .. BQ,Q−1 (a) BQ,Q (a)

← q = Q.

In (10.3), empty elements are zeros or zero matrices with appropriate sizes. Furthermore, the order of rows in matrix P(a) corresponds to the number of packets in the data queue, and matrix Bq,q (a) expresses the transition from state q to state q in the queue state when action a is taken. The details of deriving the matrix can be found in [15].

10.2.1.3

Objective Function The immediate throughput of the secondary user can be determined as follows:  T (s, a) =

pidle (a)(1 − pfalse (a))ptran su (a), 0,

if(e ≥ etran su ) and (q > 0), otherwise.

(10.4)

Here, a packet is transmitted successfully iff the secondary user has data and sufficient energy, and the sensed channel is idle and there is no false alarm.

10.2.1.4

Problem Formulation

In this section, we aim to find an optimal policy χ ∗ for the secondary user to determine the best action, i.e., which channel should be sensed, at each state such that its average throughput is maximized. Then, we can define the optimization problem for the secondary user by 1 E (T (sk , ak )) , t t

max J (χ ) = lim inf χ

t→∞

(10.5)

k=1

where J (χ ) is the average throughput of the secondary user and T (sk , ak ) is an immediate throughput function at time step k. Then, by using the linear programming (LP) technique [19], we can convert the optimization problem to an equivalent LP form as follows: Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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max

φ(s,a)

subject to



φ(s, a)T (s, a)

s∈S a∈A



φ(s , a) =

a∈A





φ(s, a)Ps,s (a),

s ∈ S,

s∈S a∈A

φ(s, a) = 1,

φ(s, a) ≥ 0,

(10.6)

s∈S a∈A

where φ ∗ (s, a) is the solution of the LP problem that represents the steady-state probability at which the secondary user is at state s and and action a is taken, and Ps,s (a) denotes the element of matrix P(a) as defined in (10.3). Then, we can obtain the optimal randomized channel selection policy as follows: φ ∗ (s, a) , for s ∈ S. (10.7) χ ∗ (s, a) =  ∗  a ∈A φ (s, a )

10.2.1.5

Performance Measures Various performance measures can be obtained as follows. 1.

Average number of packets: q=

Q  E 

qφ ∗ ((e, q), a).

(10.8)

a∈A q=0 e=0

2.

Average throughput: τ=

Q  E  a∈A q=1

3.

∗ pidle (a)(1 − f false (a))ptran su (a)φ ((e, q), a).

(10.9)

e=etran su

Average delay: d=

q , τ

(10.10)

where τ is the effective arrival rate, which is the same as the throughput.

10.2.2

Learning Algorithm In Section 10.2.1, we assume that the secondary user has some environment parameter information, e.g., idle channel probabilities and successful transmission probabilities. Nevertheless, in practice these items of information might not be available in advance, and thus we study a learning algorithm that helps the secondary user to make optimal decisions through interaction with the environment.

10.2.2.1

Problem Formulation Figure 10.4 illustrates the learning process of the secondary user through interactions with the environment to obtain the optimal policy. In Figure 10.4, there are two main

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Figure 10.4 The learning process through interactions with the environment of the secondary user.

blocks implemented for the secondary user, namely the learning algorithm and the controller. The first block, i.e., the learning algorithm, is responsible for updating and maintaining the channel access policy, while the second block, i.e., the controller, is used to instruct the secondary user to take actions. The general workflow is as follows. 1. 2. 3.

In accord with the initial setup policy, the learning algorithm will guide the controller to opt to sense one of the channels. Depending on the status obtained from the selected channel, the controller will perform a data transmission process or an energy harvesting process. The controller observes the results obtained, and then the learning algorithm updates the channel access policy on the basis of that information.

As in [21–23], we adopt a well-known randomized parameterized policy μ to determine an action at each state for the secondary user. Under μ , if the current state of the secondary user is s, the action a will be taken with the probability   exp s,a ,  μ (s, a) =  (10.11) a ∈A exp s,a where is the parameter vector of the learning algorithm, defined as = [ · · · s,a · · · ] . Here, μ (s, a) must not be negative, and must satisfy the following condition:  μ (s, a) = 1. (10.12) a∈A

Under the randomized parameterized policy μ (s, a), the transition probability function and the immediate throughput function will be parameterized as follows:  μ (s, a)Pa (s, s ) (10.13) P (s, s ) = a∈A

and R (s) =



μ (s, a)R(s, a).

(10.14)

a∈A

The aim of the secondary user is to maximize the average throughput function under the randomized parameterized policy μ (s, a), which is denoted by ψ( ). We then make two important assumptions for the learning algorithm as follows. Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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assumption 1. The Markov chain is aperiodic and there exists a state s† that is recurrent for every such Markov chain. assumption 2. For every state s, s ∈ S, the transition probability function P (s, s ) and the immediate throughput function R (s) are bounded, twice differentiable, and have bounded first and second derivatives. The first assumption is to ensure the Markov property for the system, while the second assumption will be useful when we use the gradient method. Then, the parameterized average throughput is defined as follows: ) ( t  1 R (sk ) , (10.15) ψ( ) = lim E t→∞ t k=0

where E [·] is the expectation of the throughput. Under Assumption 1, ψ( ) is well defined for every , and it does not depend on the initial state s0 . Moreover, the following balance equations hold:  π (s)P (s, s ) = π (s ), for s ∈ S, s∈S



π (s) = 1,

(10.16)

s∈S

where π (s) is the steady-state probability for the state s under the parameter vector .   These balance equations have a unique solution  = · · · π (s) · · · . After that, the average throughput can be represented as follows:  π (s)R (s). (10.17) ψ( ) = s∈S

10.2.2.2

Policy Gradient Method To express the relation between the average throughput and the immediate throughput, we first define the differential throughput d(s, ) at state s as follows: ) (T−1  (10.18) d(s, ) = E (R (sk ) − ψ( )) |s0 = s , k=0

where T = min{k > 0|sk = s† } is the first future time at which state s† is visited. Under Assumption 1, the differential throughput d(s, ) is a unique solution of the following Bellman equation:  P (s, s )d(s , ), (10.19) d(s, ) = R (s) − ψ( ) + s ∈S

for all s ∈ S. Given the differential throughput d(s, ), the gradient of the average throughput ψ( ) with respect to the parameter vector can be derived as in Proposition 10.1. Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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proposition 10.1. Let Assumptions 1 and 2 hold. Then ∇ψ( ) =



   π (s) ∇R (s) + ∇P (s, s )d(s , ) .

(10.20)

s ∈S

s∈S

The proof of Proposition 10.1 is provided in [15]. From Proposition 10.1 and [24], we can derive the standard form for the idealized gradient algorithm as follows: k+1 = k + ρk ∇ψ( k ),

(10.21)

where ρk is a learning step size. Basically, for a learning algorithm using the policy gradient method, the learner initializes a randomized parameter vector 0 ∈ R|s| , and uses this parameter vector to make a decision. Then, the basis of on information received, the learner will update the parameter vector at each step size. It was proved in [24] that, if the step size ρk satisfies Assumption 2, then limk→∞ ∇ψ( k ) = 0, and thus ψ( k ) converges. assumption 3. The step size ρk is deterministic, non-negative, and satisfies the following condition: ∞ 

ρk = ∞ and

k=1

10.2.2.3

∞ 

(ρk )2 < ∞.

(10.22)

k=1

Learning Algorithm In (10.21), if the gradient ∇ψ( k ) can be calculated at each time step, then we can find the optimal value of which maximizes the average throughput ψ( k ). Nevertheless, for large-scale systems, e.g., a large stage space, it is intractable to derive the exact gradient ∇ψ( k ). Thus, we will study an approximation solution that can estimate the gradient ψ( k ) and update the parameter vector accordingly in an online fashion.   From (10.12), we have a∈A μ (s, a) = 1, so we can derive that a∈A ∇μ (s, a) = 0, ∀ . From (10.14), we have ∇R (s) =



∇μ (s, a)R(s, a)

a∈A

=



∇μ (s, a)(R(s, a) − ψ( )),

(10.23)

a∈A

 since a∈A ∇μ (s, a) = 0. Moreover, we have 

∇P (s, s )d(a , ) =

s ∈S



∇μ (s, a)Pa (s, s )d(s , ),

(10.24)

s ∈S a∈A

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Therefore, along with Proposition 10.1, we can derive the gradient of ψ( ) as follows:       π (s) ∇R (s) + ∇P (s, s )d(s , ) ∇ψ( ) = s∈S

=



 π (s)

s∈S

s ∈S



  ∇μ (s, a) R(s, a) − ψ( )

a∈A

+





=

π (s)

s∈S

=







∇μ (s, a)Pa (s, s )d(s , )

s ∈S a∈A





∇μ (s, a)

 

   R(s, a) − ψ( ) + Pa (s, s )d(s , ) s ∈S

a∈A

π (s)∇μ (s, a)q (s, a),

(10.25)

s∈S a∈A

where

   Pa (s, s )d(s , ) q (s, a) = R(s, a) − ψ( ) + s ∈S ) (T−1   = E R(sk , ak ) − ψ( ) |s0 = s, a0 = a .

(10.26)

k=0

Here T = min{k > 0|sk = s† } is the first future time at which the state s† is visited, and q (s, a) is the differential throughput at state s when action a is chosen on the basis of policy μ . Then, we present Algorithm 10.1 that updates the parameter vector at visits to the recurrent state s† . Algorithm 10.1 The learning algorithm updates the parameter vector at visits to the recurrent state s† At time step km+1 of the (m + 1)th visit to state s† , we update the parameter vector  as follows: and the estimated average throughput ψ m ), m+1 = m + ρm Fm ( m , ψ m+1 = ψ m + κρm ψ

(10.27)

km+1 −1 



m R(sk , ak ) − ψ

 (10.28)

k =km

where m ) = Fm ( m , ψ

km+1 −1



 q m (sk , ak )

k =km

 q m (sk , ak ) =

km+1 −1 



∇μ m (sk , ak ) , μ m (sk , ak )

 m . R(sk , ak ) − ψ

(10.29)

(10.30)

k=k

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Here, to update the parameter vector , we estimate the gradient of the average m ) which computes the total throughput by using the estimation function Fm ( m , ψ estimated value of the gradient of the average throughput between two successive visits (i.e., the mth and (m + 1)th visits) to the recurrent state s† . In Algorithm 10.1, κ is a positive constant and ρm is a step size parameter. We then derive the following convergence result for Algorithm 10.1. proposition 10.2. If Assumptions 1–3 are satisfied, and if ( 0 , 1 , . . . , ∞ ) is the sequence of parameter vectors generated by Algorithm 10.1, then ψ( m ) converges and lim ∇ψ( m ) = 0,

m→∞

(10.31)

with probability one. The proof of Proposition 10.2 is given in [15]. In Algorithm 10.1, in order to update the value of the parameter vector at the next visit to the state s† , we need to store all of the values of  q m (sn , an ) and ∇μ m (sn , an )/μ m (sn , an ) between two successive visits. However, this method could result in slow processing. Therefore, we modify Algorithm 10.1 to improve m ) as follows: the efficiency. First, we re-write Fm ( m , ψ m ) = Fm ( m , ψ

km+1 −1



 q m (sk , ak )

k =km

∇μ m (sk , ak ) μ m (sk , ak )

km+1 −1

 ∇μ (sk , ak ) km+1 −1   m m R(sk , ak ) − ψ μ m (sk , ak )  

=

k =km

km+1 −1

=

(10.32)

k=k

 

 m zk+1 , R(sk , ak ) − ψ

k =km

where zk+1 =



∇μ m (sk , ak )/μ m (sk , ak ), if k = km , zk + ∇μ m (sk , ak )/μ m (sk , ak ), k = km + 1, . . . , km+1 − 1.

(10.33)

Then, we derive the online learning algorithm which updates the value of the parameter vector at each time step on the basis of the information observed at the current state as presented in Algorithm 10.2. In Algorithm 10.2, ρk is the step size of the algorithm satisfying Assumption 3.

10.2.3 10.2.3.1

Performance Evaluation Parameter Setting For the learning algorithm, we use the following parameters for performance evaluation. We assume that, at the beginning of Algorithm 10.2, the secondary will start with a randomized policy, where the secondary user will select channels 1 and 2 with the same probability of 0.5. We set the initial value of ρ = 0.0005, and it will be updated

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Table 10.1. Setup parameters Parameter

Notation

Value

Maximum data queue size Maximum energy queue size Number of channels The idle channel probability of channel 1 The idle channel probability of channel 2 Energy to transmit 1 packet Packet arrival probability Successful packet transmission probability Successful harvesting energy on channel 1 Successful harvesting energy on channel 2

Q E C pidle 1 pidle 2 etran su λ psu tran p1har p2har

10 packets 10 units 2 0.1 0.9 1 unit 0.5 0.95 0.95 0.7

Algorithm 10.2 The online learning algorithm which updates at every time step ( k ) are available from At time step k, the state is sk , and the values of k , zk , and ψ  the previous iteration. We update zk , , and ψ according to  ∇μ k (sk , ak )/μ k (sk , ak ), if sk = s† , zk+1 = (10.34) zk + ∇μ k (sk , ak )/μ k (sk , ak ), otherwise, k )zk+1 , k+1 = k + ρk (R(sk , ak ) − ψ k + κρk (R(sk , ak ) − ψ k ). k+1 = ψ ψ

(10.35) (10.36)

after every 18,000 iterations as follows: ρk+1 = 0.9ρk . We also set κ = 0.01. Other parameters are set up as in Table 10.1. To evaluate the performance of the secondary user we compare the average throughput obtained by the learning algorithm with that of the cases with complete information, incomplete information, and random policy. The complete information policy [18] is used as an upper-bound performance when the secondary user has perfect information about the surrounding environment. For the incomplete information policy, the secondary user just knows the channel status distribution probability in advance, and thus it will adopt the optimal policy given in Section 10.2.1. The learning algorithm, i.e., Algorithm 10.2, is used when the secondary user has no information, and it has to make decisions on the basis of its learning process. Finally, the random policy will access channels randomly with the same probability of 0.5.

10.2.3.2

Numerical Results Policies from MDP-Based Optimization Formulations In Figures 10.5(a), (b), and (c), we show policies obtained when the secondary user has incomplete information, complete information when channel 1 is idle and channel 2 is busy, and complete information when channel 1 is busy and channel 2 is idle, respectively. The z-axis represents the probability of choosing channel 1. In Figure 10.5(a), when the secondary user has incomplete information, it will select channel 1 when the

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(a)

(b)

353

(c)

Figure 10.5 Policy of the secondary user for (a) the case of incomplete information, (b) complete information when channel 1 is idle and channel 2 is busy, and (c) complete information when channel 1 is busy and channel 2 is idle.

energy level is low and the number of packets in the data queue is small because of the low idle channel probability of channel 1, i.e., the secondary user can harvest more energy from channel 1. On the other hand, when the number of packets in the data queue and the energy level are high, the secondary use will select channel 2 because channel 2 has a higher idle probability, and thus it is preferable for transmitting data. In Figure 10.5(b), the secondary user almost always selects channel 1, except when the data queue or energy storage is empty. This is because the secondary user can always harvest energy from channel 2, thus it will prioritize data transmission to maximize its throughput. Nevertheless, in Figure 10.5(c), when channel 1 is busy and channel 2 is idle, the secondary user selects channel 1 only when the energy level is low and the number of packets in the data queue is small. This result can be explained in a similar way to that of the incomplete information case.

Convergence of the Learning Algorithm In Figure 10.6, we show the convergence of the proposed learning algorithm when the number of channels is varied. As shown in Figure 10.6, as the number of channel increases, the convergence rate of the learning algorithm and the average throughput of the secondary user are slightly slower. This is because, when the number of channels is large, the secondary user has more actions to learn, resulting in a longer learning process and leading to a poorer performance. For more analysis on the convergence of the proposed learning algorithm, please refer to [15].

Throughput Performance We then vary the packet arrival probability and the idle channel probability of channel 1 to evaluate the performance of the secondary user in terms of the average throughput obtained. In Figure 10.7(a), when the packet arrival probability is less than 0.4, all of the policies yield almost the same throughput because in this case the secondary user can harvest sufficient energy and has adequate opportunities to transmit its packets. However, when the packet arrival probability is high, the complete information policy achieves the highest throughput, followed by the incomplete information policy, the proposed learning algorithm, and the random policy, in that order. The reason is that Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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Average throughput (packets/time slot)

0.46 0.45 0.44 0.43 0.42 0.41 2 channels 3 channels 4 channels

0.4 0.39 0

100

200

300

400

500

600

700

800

Iterations (x104)

Figure 10.6 The convergence of the learning algorithm when the number of channels is varied.

(b) 0.5

0.45 0.4 0.35 0.3 0.25

Random policy Learning algorihtm Incompleted information case Completed information case

0.2 0.15 0.1 0.1

0.2

0.3

0.4

0.5

0.6

Packet arrival probability

0.7

0.8

0.9

System throughput (packets/time slot)

System throughput (packets/time slot)

(a)

0.5 0.45 0.4 0.35 0.3 0.25 0.2

Random policy Learning algorihtm Incompleted information case completed information case

0.15 0.1 0.05 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Idel channel -1 probability

Figure 10.7 The average throughput of the system when (a) the packet arrival probability is varied and (b) the idle channel probability for channel 1 is varied.

the complete information policy can perfectly exploit the channel status to obtain the best performance, while for the incomplete information policy the secondary user has to optimize its policy according to the dynamic of the channels. We observe that the learning algorithm yields a throughput that is close to those of the policies obtained from the optimizations, and much higher than that of the random policy. It is important to note that when the arrival probability is higher than 0.5 the system reaches a saturated state and thus the average throughput is not increased. In Figure 10.7(b), as the idle channel probability of channel 1 increases, the average throughputs of policies decrease. The reason is that the idle channel probability of channel 2 is very high, i.e., 0.9, and thus, if the idle channel probability of channel 1 is low, the secondary user is able to harvest more energy from channel 1. However, if the idle channel probability of channel 1 is also high, the amount of energy harvested will be reduced dramatically, resulting in a low throughput for the secondary user. Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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Figure 10.8 System model for cooperative multiuser in a RF-powered cognitive radio network.

10.3

Performance Optimization for Cooperative Multiuser Cognitive Radio Networks with RF Energy Harvesting Capability In the first section, we introduce optimal channel access policies for one secondary user in an RF-powered cognitive radio network. In this section, we will discuss the cooperation problem among secondary users in order to maximize their overall performance. Differently from Section 10.2, in this section, we consider an RF-powered cognitive radio network where there are N multiple secondary users and C channels allocated to primary users as illustrated in Figure 10.8. As in Section 10.2, the maximum data queue size, the maximum energy queue size, and the packet arrival probability are denoted by Qn , En , and λn , respectively. Other model parameters, such as missed detection, a false alarm, and so on, are denoted the same as in Section 10.2. In the following, we study two multi-access schemes for the cooperative secondary users. In Section 10.3.1, we apply the learning algorithm used in Section 10.2 for secondary users in a round-robin fashion. Then, in Section 10.3.2, we will examine a decentralized learning algorithm that has been developed from the learning algorithm presented in Section 10.2.

10.3.1

TDMA Learning Algorithm First, we study how to apply the time division multiple access (TDMA) protocol for the multi-access problem of secondary users under multiple channels. In particular, the

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secondary users are scheduled to use channels, i.e., harvest energy or transmit data, in a round-robin fashion. We then adopt the learning algorithm proposed in Section 10.2 for the secondary users to make optimal decisions in order to adapt to environment conditions.

10.3.1.1

Problem Formulation We define the state space of the secondary user n as follows:1   S = (e, q, ϑ); e ∈ {0, 1, . . . , E}, q ∈ {0, 1, . . . , Q}, ϑ ∈ {0, 1} .

(10.37)

As in Section 10.2, the state space of a secondary user consists of two variables, i.e., the energy level e and the number of packets q. However, in this case, the state space of the secondary user is included by the time schedule variable ϑ which indicates that the secondary user is not in schedule or in schedule (corresponding to ϑ = 0 or ϑ = 1, respectively). Then, the state space can be represented by a composite variable s = (e, q, ϑ) ∈ S. The action space A is defined in the same way as in Section 10.2, in which each secondary user has to make a decision a ∈ A = {0, 1, . . . , C} to select one of the channels to sense. When a = 0, the secondary user will do nothing. Similarly, the immediate reward function for each secondary user will be defined as the number of bits successfully transmitted. Then the immediate reward function R and the parameterized average throughput ψ( ) of the secondary user n can be expressed in the following way:  1, if a packet is transmitted successfully, R(s, a) = (10.38) 0, otherwise, and

) ( t  1 ψ( ) = lim E T (sk , k ) . t→∞ t

(10.39)

k=0

Now, the problem becomes how to optimize performance for secondary users and, similarly to what we did in Algorithm 10.2 in Section 10.2.2, we derive a learning algorithm (i.e., Algorithm 10.3) that allows secondary users to update the parameter vector at each time step by estimating the gradient of the average throughput. In Algorithm 10.3, κ is a positive constant and ρk is the step size of the algorithm. The convergence of Algorithm 10.3 can be proved in a similar way to Appendix B in [15]. However, we need to note that, differently from Algorithm 10.2, the recurrent state in Algorithm 10.3 is determined by s† = (e† , q† , ϑ † ). This means that a secondary user will update its learning parameters if and only if its energy level, number of packets, and time schedule are revisited in the same time slot.

1 We omit the indicator of secondary users in this section for brevity of presentation.

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Algorithm 10.3 Online learning algorithm that updates parameter vector at every time step ( k ) are available from At time step k, the state is sk , and the values of k , zk , and ψ  the previous iteration. We update zk , k , and ψ according to  ∇μ k (sk , ak )/μ k (sk , ak ), if sk = s† , zk+1 = (10.40) zk + ∇μ k (sk , ak )/μ k (sk , ak ), otherwise, k )zk+1 , (10.41) k+1 = k + ρk (R(sk , ak ) − R k+1 = R k + κρk (R(sk , ak ) − R k ). R

10.3.2

(10.42)

Decentralized Learning Solution In this section, we study the case where secondary users are cooperative in a decentralized manner. First, a decentralized partially observable Markov decision process (DEC-POMDP) [25] is adopted to model the cooperative optimization problem among secondary users. Then, we propose a decentralized learning algorithm to obtain optimal policies for secondary users in an online fashion.

10.3.2.1

Optimization Formulation We formulate the optimization problem for the RF energy harvesting cognitive radio network with multiple secondary users and multiple channels (i.e., the multipleuser multiple-channel (MUMC) case) as a DEC-POMDP in a discrete time system. A general DEC-POMDP model can be defined as a tuple N, S, A, P, R, O, O, where • • • • • • •

10.3.2.2

N is the total number of secondary users, S is a global state space of the secondary users, A is a global action space or a set of joint actions, P is a joint transition probability function, R is the immediate global reward function, O is a finite set of joint observations, and O is a joint observation probability function.

State Space We define S  (S1 × · · · × Sn × · · · × SN ) as the global system state space, where Sn is the local state space of secondary user n which can be defined as follows:   (10.43) Sn = (en , qn ); en ∈ {0, 1, . . . , En }, qn ∈ {0, 1, . . . , Qn }, , where en and qn express the energy level and the number of packets of the secondary user n, respectively. Again, En is the maximum energy queue size and Qn is the maximum data queue size. Then, the local state of secondary user n is defined as a composite variable sn = (en , qn ) ∈ Sn .

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10.3.2.3

Action Space The global action space or joint action space A is a composition of sets of local action spaces from secondary users. Thus, the global action space can be defined by A  (A1 × · · · × An × · · · × AN ),

(10.44)

where An is defined the same as in Section 10.3.1, i.e., it is a set of available channels for secondary user n to choose from. Hence, at each time epoch, the secondary user n has to make a decision an ∈ An = {0, 1, . . . , C} to select a channel to sense or to do nothing.

10.3.2.4

Transition Probability Function By using the simulation-based method, under a control policy , the joint transition probability function P can be determined from the transition probability of the local state of the secondary users (i.e., a queue state and an energy state) as follows:       (10.45) P s(t + 1)|s(t),  = Penv P e(t + 1), q(t + 1)  e(t), q(t) ,  , where Penv is the probability function of environment parameters that can be generated by the simulator. s(t) ∈ S denotes the joint state of the system at time slot t. q(t) and e(t) denote the joint queue state and the joint energy state at time slot t, respectively.     P e(t + 1), q(t + 1)  e(t), q(t) ,  is the joint transition probability of secondary users, and this probability can be derived from the transition probability of the local states (i.e., the queue state and energy state of secondary users) as follows:     P e(t + 1), q(t + 1)  e(t), q(t) ,  =      /N ∗ ∗ n=1 P en (t), qn (t) P an (t) , if en (t + 1) = En , qn (t + 1) = Qn , (10.46) 0, otherwise,     where Qn∗ = min [qn (t) − qtrn (t)]+ + λn (t) , Qn and En∗ = min en (t) − etrn (t)]+ +   tr ehar n (t) , En . Here, qn (t) is the number of packets transmitted by secondary user n at time step t, λn (t) is the number of arriving packets, ehar n (t) is the amount of energy harvested, and etrn (t) is the amount of energy consumed at time slot t. Moreover, [x]+ = max(x, 0).

10.3.2.5

Immediate Global Reward Function In this section, secondary users aim to maximize the overall network throughput, and thus the immediate global reward function is defined as the total number of successfully transmitted packets at time slot t, which is given by R(s(t), a(t)) =

N  n=1

R(sn (t), an (t)) =

N 

Rn (t).

(10.47)

n=1

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10.3.2.6

359

Observations and Observation Probability Function In our proposed system model, the observation of each secondary user at each time slot is its local information from the data queue and the energy storage, i.e., its current state. Thus, the observation probability function can be defined in the same way as in (10.46).

10.3.2.7

Parameterization for DEC-POMDP As in Section 10.2.2, we use a parameterized randomized policy [21–23]. Under the parameterized randomized policy, when secondary user n is at state sn , the secondary user will select action an with the probability μ n (sn , an ) given as follows:   exp θsn ,an ,  (10.48) μ n (sn , an ) =  ai ∈An exp θsn ,ai where n = {θsn ,an ∈ R} is the parameter vector of secondary user n at state sn .  Moreover, every μ n (sn , an ) must not be negative and an ∈An μ n (sn , an ) = 1, ∀n. Under the parameterized randomized policies of the secondary users, the joint transition probability function and the average cost criterion can be parameterized as follows:  P(s |s, ( )) = μ (s, a)P(s |s, a), (10.49) a∈A

and R(s, ) =



μ (s, a)R(s, a),

(10.50)

a∈A

/N

where μ (s, a) = n=1 μ n (sn , an ) and is a joint parameter vector of the system. Then, we can define the parameterized average reward by ) ( T    1 R( ) = lim sup E( ) R s(t), ) , (10.51) T→∞ T t=1

where T is the total time horizon. In this section, we consider the case where secondary users want to cooperate to maximize the overall network throughput by obtaining the jointly optimal control policy ( ). Nevertheless, their decisions are made on the basis of their local information, resulting in a partially observable optimization problem where the control policy n ( n ) is a function of a local state only. In addition, in order to control the energy consumption for the sensing process of secondary user n which does not exceed a threshold Wn∗ per time slot, the following constraints must be satisfied: W n ≤ Wn∗ ,

∀n.

(10.52)

Consequently, the optimization problem with constraints can be defined as follows: ) ( T N     1 max R( ) = R n ( ) = lim sup E( ) R s(t), ) , T→∞ T n=1

subject to W n (( )) = W n ( ) ≤ Wn∗ , ∀n,

t=1

(10.53)

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where R(s(t), ) is the parameterized common immediate throughput generated at the joint state s(t) after the joint action a(t) has been taken, and R( ) is the parameterized average total throughput. W n denotes the average energy consumption for the sensing channels of secondary user n and Wn∗ denotes the target threshold that we want to control.

10.3.2.8

Lagrange Multiplier and Policy Gradient Method In order to address the optimization problem with constraints defined in (10.53), the Lagrange multiplier method is adopted. First, we define the Lagrange function as follows: L ( , γ ) =

N    R n ( ) + γn (W n ( ) − Wn∗ ) ,

(10.54)

n=1

where γn is a Lagrange for the constraint of secondary user n. If we denote   multiplier       ∗ G s, a = N + γ W as the immediate value function, then , a − W R s n n n n n n=1 the parameterized immediate value function will be      G s, = μ (s, a)G s, a . (10.55) a∈A

Then, the following balance equations hold:  πs ( )P(s |s, ( )) = πs ( ), for s ∈ S, s∈S



πs ( ) = 1,

(10.56)

s∈S

where πs ( ) is the steady-state probability of joint state s under the parameter vector . These balance equations have a unique solution defined as a vector  =   . Thus, the Lagrange function can be represented as follows: · · · πs ( ) · · · L ( , γ ) =



  πs ( )G s, .

(10.57)

s∈S

Then, to solve the Lagrange function, we use Karush–Kuhn–Tucker (KKT) conditions [26] to find a local optimal solution ∗ that satisfies the following conditions: ∇ L ( ∗ , γ ∗ ) = 0, W n ( ∗ ) − Wn∗ ≤ 0, γn∗ (W n ( ∗ ) − Wn∗ ) = 0, ∀n,

(10.58)

γn∗ ≥ 0. To obtain the gradient of the Lagrange function L ( , γ ), we first define the differential cost d(s, a, ) at state s under a control action a and the parameter vector as follows: Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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) (T−1      d(s, a, ) = E( ) G s(t), a(t) − L ( , γ ) s(0) = s, a(0) = a , (10.59) t=0

where T = min{t > 0|s(t) = s† } is the first future time at which state s† = (s†1 , . . . , s†N )        ∗ . s† can be is visited and G s(t), a(t) = N n=1 R sn (t), an (t) + γn Wn (t) − Wn   selected randomly from state space S. Here, R sn (t), an (t) is the number of packets successfully transmitted by secondary user n and Wn (t) is the energy used by secondary user n at time slot t. In (10.59), d(s, a, ) can be expressed as the differential cost if action a is carried out on the basis of policy μ at state s. We can then obtain the gradient of the Lagrange function L ( , γ ) as in Proposition 10.3. proposition 10.3. The gradient of the Lagrangian function is determined as follows: ∇ n L ( , γ ) =



πs ( )μ (s, a)

s∈S a∈A

∇ n μ n (sn , an ) d(s, a, ), μ n (sn , an )

(10.60)

where πs ( ) is the steady state probability of state s ∈ S and μ (s, a) = μ n (sn , an ).

/N n=1

The proof of Proposition 10.3 is provided in Appendix A in [16]. Then, in accord with Proposition 10.3, secondary users will update their parameter vectors on the basis of the idealized gradient algorithm at each time step t as follows [24]: = tn + ρt ∇ n L ( , γ ), t+1 n

∀n

(10.61)

where ρt is a suitable step size that satisfies the following assumption. assumption 4. The step size ρt is deterministic, non-negative, and satisfies the following conditions: ∞  t=1

10.3.2.9

ρt = ∞ and

∞ 

(ρt )2 < ∞.

(10.62)

t=1

Decentralized Online Learning Algorithm with Communications By using the idealized gradient method, the joint optimal policy for secondary users can be obtained from (10.61). Nevertheless, to update their local parameter vector n , secondary users need to know the Lagrange function L ( , γ ) in order to calculate their partial differential equation. Moreover, secondary users also need to calculate the gradient of the Lagrange function L ( , γ ) with respect to n at every time step, which is intractable if the system has a large state space. Thus, in this section, we present a decentralized online learning algorithm with a small communication overhead that can estimate the gradient of the Lagrange function instead of computing its exact value. Then, the secondary users can update their parameter vectors independently and in parallel as shown in Algorithm 10.4.

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Algorithm 10.4 Decentralized online learning algorithm with communications 1. 2.

3.

4.

5.

Initialization. Each secondary user determines the local parameter vector 0n . Sensing and decision epoch. At the beginning of each time slot, the secondary user makes a decision to sense a target channel according to the information from its local state (i.e., the number of packets and the energy level). If the sensed channel is busy and the energy storage of the secondary user is not full, the secondary user will harvest RF energy. By contrast, if the sensed channel is idle, and the energy queue and the data queue are not empty, then the secondary user will transmit a packet. Otherwise, the secondary user does nothing. Channel processing. After decisions have been made, the secondary users perform RF energy harvesting or packet transmission according to the decisions made in the sensing and decision phases. Information sharing. At the end of each time slot, each secondary  user deter mines its local current state and shares the information In = R sn (t), an (t) + γn (Wn (t) − Wn∗ ). If the current state of secondary user n is s†n , the user will also send a state synchronization signal υn to the other secondary users. Updating parameter n . Each secondary user updates the local parameter n as follows:   t ztn , t+1 = tn − α(t) IG − L (10.63) n N where IG = n=1 In is the current total value of the Lagrange functions of t is the estimated total value of Lagrange functions, which secondary users and L is updated as follows:   t+1 = L t − α(t) IG − L t , L (10.64) where α(t) is the step size satisfying Assumption 5, and  ∇ n μ n (sn , an )/μ n (sn , an ), if s† is visited, t+1 zn = t zn + ∇ n μ n (sn , an )/μ n (sn , an ), otherwise.

6.

(10.65)

Updating Lagrangian multiplier γn . Each secondary user updates the local Lagrangian multiplier {γn } as follows:     γnt+1 = max γnt + β(t) Wn (t) − Wn∗ , 0 , (10.66) where β(t) is the step size satisfying Assumption 5.

In step 4 of Algorithm 10.4, to lessen the communication load for the network, a secondary user just needs to send a state synchronization signal when its current state is its recurrent state.2 assumption 5. The step sizes α(t) for updating parameter vectors and β(t) for updating Lagrangian multipliers are deterministic, non-negative, and satisfy the following conditions: 2 In the case when state s† is visited, each secondary user will receive all messages from all other users to notify that they are in recurrent state s†n .

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∞  t=1

α(t) =

∞ 

β(t) = ∞,

t=1

∞   t=1

363

 β(t) α 2 (t) + β 2 (t) < ∞, and → 0. α(t)

The last condition, i.e., β(t)/α(t) → 0, implies that the sequence {β(t)} → 0 faster than the sequence {α(t)}. For example, we can choose α(t) = 1/t2/3 and β(t) = 1/t or α(t) = 1/t and β(t) = 1/(1 + t log t), and so on [27]. With Algorithm 10.4, the secondary users can make decisions on the basis of their local information and exchanged messages (i.e., In and υn defined in Algorithm 10.4). Appendix B in [16] provides an analysis and the proof of convergence for Algorithm 10.4.

10.3.3

Performance Evaluation In this section, we use MATLAB to carry out simulations to evaluate the performance of the proposed learning algorithms for cooperative secondary users.

10.3.3.1

Simulation Setup We first consider the scenario in which there are two primary channels and two secondary users who want to cooperate to maximize their overall throughput. In this scenario, we will show the convergence of two proposed learning algorithms, i.e., a TDMA learning algorithm (TDMA-LA) and a decentralized learning algorithm (DLA), along with their optimal policies. Then, the number of secondary users will be increased, and two other schemes, namely a greedy policy (GP) and a threshold policy (TP), will be used to evaluate the efficiency of these proposed learning algorithms. For the GP, the secondary users will transmit data as long as they have data and enough energy for data transmission. Otherwise, they will harvest energy. For the TP, the secondary users will transmit data iff they have data and their energy levels are higher than a safety level, and in this case the safety level for secondary user n is set at %En /2&, where %·& is the floor function. Under the threshold policy, secondary users can reserve a certain amount of energy to serve for data transmission when the channel is idle. Also, this policy is efficient at reducing collisions among secondary users when the number of available licensed channels is limited. Both for the GP and for the TP, it is assumed that secondary users have information about the idle channel probability of channels in advance. As a result, when a secondary user wants to transmit data, it will choose to sense the channel with higher channel idle probability, whereas, when it wants to harvest energy, it will opt to sense the channel with lower idle probability. Other parameters are set as in Table 10.2.

10.3.3.2

Simulation Results We first show the convergence and optimal policies obtained by the TDMA-LA, i.e., Algorithm 10.3, and the DLA, i.e., Algorithm 10.4 for the case with two secondary users and two primary channels. It is shown in Figure 10.9 that the convergence of the TDMA-LA is relatively faster than that of the DLA. In particular, the average throughput of the TDMA-LA converges to 0.7 after 2 × 106 iterations, while that of

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Table 10.2. Setup parameters Parameter

Notation

Value

Maximum data queue size Maximum energy queue size Idle channel probability of channel 1 Idle channel probability of channel 2 Idle channel probability of channel 3 (Scenario 1) Idle channel probability of channel 3 (Scenario 2) Energy to transmit one packet Packet arrival probability Successful packet transmission probability Successful harvesting energy on channels False-alarm probability Missed detection probability The initial parameter vector

Q E pidle 1 pidle 2 pidle 3 pidle 3 etran su λ psu tran p1har pfalse pmiss 0

5 packets 5 units 0.2 0.8 0.2 0.8 1 unit 0.5 0.95 0.95 0.01 0.01 0

(b)

(a)

0.5

0.65 0.6

The average throughput of secondary user 1 The average throughput of secondary user 2

0.55

The average throughput of the network

0.5 0.45 0.4 0.35 0.3

Average throughput (packets/time slot)

Average throughput (packets/time slot)

0.7

0.45 0.4

The average throughput of secondary user 1 The average throughput of secondary user 2

0.35

The average throughput of the network

0.3 0.25 0.2 0.15 0.1

0.25 0

200

400

600 4

Iterations (x10 )

800

1000

0

200

400

600

800

1000

4

Iterations (x10 )

Figure 10.9 The convergence of (a) the TDMA learning algorithm and (b) the decentralized learning algorithm.

the DLA is approximately 0.46 after 4 × 106 iterations. The reason is that the learning process of the DLA is more complicated than that of the TDMA-LA. Specifically, for the DLA, a secondary user has to experience three learning processes. First, given the current state, the secondary user has to learn whether it should harvest energy or transmit data. Second, the secondary user also has to learn which is the best channel to sense. For example, through interactions with the environment, the secondary user will learn which channel has the highest idle channel probability, and thus, when it wants to transmit data, this channel will be the one selected to sense. Third, the secondary user also needs to learn the behaviors of others in the network because of the random access process. For TDMA learning, secondary users just have to experience the first Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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Probability of sensing channel –1

0.8 0.6 0.4 0.2 0 0 1

2 3

4 Number of packets in queue

5

6

7

5

3

4

2

1

0

Probability of sensing channel –1

(b)

(a)

1 0.8 0.6 0.4 0.2 0 5 4 3 2 1

Energy level

1

0

0

2

3

4

5

6

7

Energy level

Number of packets in queue

Figure 10.10 The policy of secondary user 1 obtained by the TDMA learning algorithm for the

cases in which (a) it is not scheduled and (b) it is scheduled to access a time slot. (b)

0.8 0.6 0.4 0.2 0 0 1

0

2

1

3 3

4 5

Number of packets in queue

2

1 0.8 0.6 0.4 0.2 0 5 4 3 2 1

4 5

Probability of sensing channel–1

Probability of sensing channel–1

(a)

0

Energy level

0

1

2

3

4

5

6

7

Energy level

Number of packets in queue

Figure 10.11 The policy of secondary user 2 obtained by the TDMA learning algorithm for the

cases in which (a) it is not scheduled and (b) it is scheduled to access a time slot.

two learning processes. As a result, the convergence rate of the DLA will be slower than that of the TDMA-LA, as shown in Figure 10.9. As shown in Figure 10.9, the average throughput of both secondary users obtained by the TDMA-LA is nearly equal, while the average throughput of secondary users obtained by the DLA has a noticeable difference. This stems from the policies adopted for the learning algorithms. Specifically, as shown in Figures 10.10 and 10.11, the optimal policies obtained by the TDMA-LA for the two secondary users are almost the same, whereas they are different in the case of the DLA as shown in Figure 10.12. For the TDMA-LA, secondary users interact with the environment in sequence, and hence there is only one secondary user interacting with the environment at a time. Consequently, for the same environment and the learning algorithm, the secondary users accede the same policies to maximize their throughput. Nevertheless, for the DLA, Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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(b) Probability of sensing channel–1

Probability of sensing channel–1

(a) 1 0.8 0.6 0.4 0.2 0 5

1 0.8 0.6 0.4 0.2 0 5 4

4

3

3

2

2 1 0

Energy level

0

1

2

3

4

5

6

1 0

Energy level Number of packets in queue

0

1

2

3

4

5

6

Number of packets in queue

Figure 10.12 The policy of secondary users (a) 1 and (b) 2 obtained by the decentralized learning

algorithm.

the secondary users interact not only with the licensed channels in order to explore the environment, but also with other secondary users in order to learn their behaviors. Since the secondary users adopt the randomized parameterized policy, their actions are carried out randomly at each time step on the basis of information observed from others. Thus, the policies for the secondary users can be different, but their joint objective is maximized. It is important to note that, although the policies for the secondary users could be different, the average network throughput obtained by the DLA still converges to the same point. Then, the number of secondary users is increased to evaluate the average throughput obtained by the TDMA-LA and the DLA. We also compare the performance with the GP and TP to demonstrate the efficiency of the proposed learning algorithms. As shown in Figure 10.13, when the number of secondary users increases, the average throughput for the system obtained by the TDMA-LA is highest, and it increases when the number of secondary users increases. It becomes saturated when the number of secondary users is greater than four. Differently from TDMA-LA, the average throughput obtained by the DLA decreases as the number of secondary users increases. Here, although the average throughput of the DLA is higher than that of the GP and the TP, it is still much lower than that of the TDMA-LA. This is because of the harvesting of energy by secondary users. For the TDMA-LA, when a secondary user is not scheduled, it still can harvest energy to reserve for data transmission when its turn comes. However, for the DLA, secondary users have to contend for data transmission, thereby deceasing their energy harvesting opportunities. In addition, for the DLA, when collisions happen, secondary users will lose energy to re-transmit data, and thus the network throughput of the DLA is lower than that of the TDMA-LA, especially when the number of secondary users is high. We now increase the number of licensed channels to three and consider two cases, i.e., when the channel idle probability of channel 3 is 0.2 and 0.8. In Figure 10.14(a), when Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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0.8

Average throughput (packets/time slot)

0.7 TDMA learning algorithm Decentralized learning algorithm Greedy policy Threshold policy

0.6 0.5 0.4 0.3 0.2 0.1 0

2

3

5

4

Number of secondary users

Figure 10.13 The average throughput of the system under different algorithms with two channels.

(a)

(b) 0.75 Average throughput (packets/time slot)

Average throughput (packets/time slot)

0.9 0.8 0.7

TDMA learning algorithm Decentralized learning algorithm Greedy policy

0.6

Threshold policy

0.5 0.4 0.3

0.7 0.65 0.6 0.55 0.5 TDMA learning algorithm Decentralized learning algorithm Greedy policy

0.45

Threshold policy

0.2

0.4 2

3 4 Number of secondary users

5

2

3 4 Number of secondary users

5

Figure 10.14 The average throughput with (a) two channels with low idle probability and one

channel with high idle probability, and (b) two channels with high idle probability and one channel with low idle probability.

the idle channel probability of channel 3 is 0.2, i.e., there are two channels with low idle channel probability and one channel with high idle channel probability, the average throughputs obtained by the algorithms are similar to those for the case of one channel having high idle probability and one channel having low idle probability in Figure 10.13. However, the average throughput obtained in the former case is slightly greater than that in the latter case because now the secondary users have more opportunities to harvest energy and transmit packets. However, there are some changes when there are two channels with low idle probability and one channel with high idle probability. As shown in Figure 10.14(b), the average throughput of the DLA is improved noticeably, Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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while that of the TDMA-LA is unchanged. When the number of channels with high idle channel probability is high, secondary users have more opportunities to transmit data without collisions, thereby increasing the average throughput for the DLA. However, for the TDMA-LA, at each time slot there is only one secondary user interacting with the environment. Thus, when the number of channels increases, the network performance will not be impacted. The above results lead to the conclusion that the TDMA-LA is the most effective solution when the number of channels is small and there are many secondary users. In fact, when the number of channels becomes large and the number of secondary users is small enough, the average throughput obtained by the DLA can be greater than that of the TDMA learning algorithm.

10.4

Performance Optimization for Wireless-Powered Cognitive Radio Networks under Smart Jamming Attacks In Sections 10.2 and 10.3, we studied the performance optimization problem for secondary users in RF energy harvesting environments. However, in these networks, secondary users are vulnerable to jamming attacks because they do not own the spectrum and malicious users also can take advantage of harvesting wireless energy to launch attacks. Therefore, to deal with jamming attacks on the target channel, we discuss a solution that is based on the tactic of deception in military usage. The main idea of the deception mechanism is using fake transmissions to undermine the ability of enemies to attack, thereby rendering jammers unable to attack when secondary users transmit real information. In particular, we will consider a case where there are some secondary users (SUs) and jammers coexisting in the same environment as shown in Figure 10.15. While the secondary users want to transmit data to their destinations on a cognitive radio channel allocated by a primary user, the jammers aim to impede communication by carrying out jamming attacks. The time is slotted and the idle channel probability of the primary user in a time slot is pidle c . The SUs perform sensing at the beginning of each time slot. If the sensed channel is found to be idle, they will transmit data over the channel. Otherwise, they will do nothing. As in previous sections, we also consider the sensing errors for secondary users, called missed detection and false alarm, which have probabilities pmiss su and pfalse su , respectively. The SUs are equipped with a data buffer to store data and a battery to store energy harvested from an energy source through wireless energy harvesting techniques. We assume that, at each time slot, the energy source will transmit energy with the probability pene and that the energy harvested will then be used to transmit data in the data queue for SUs. To create favorable conditions and achieve better performance for SUs, we assume that each SU is equipped with two interfaces, one for data transmission and another for energy harvesting, and thus SUs can perform data transmission and energy harvesting independently and simultaneously. Each SU’s data queue has two states, i.e., idle and busy, corresponding to when the SU has no data and when the SU

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Figure 10.15 System model of wireless energy harvesting CRNs under smart jamming attacks.

has some data, respectively. Furthermore, each SU has an energy storage device with a capacity of Esu units of energy and, in each time slot, the user can harvest ehar su units . When the SU has energy, the SU can go to sleep mode of energy with probability phar su or transmit data if the data queue is not empty or it can perform a deception action by transmitting fake signals to the channel in order to entrap jammers. When the SU transmits data or fake information to the channel, if a jammer detects signals from SUs and it has enough energy, it will carry out an attack by jamming the channel. Here, we assume that jammers are intelligent and that they are able to distinguish between signals transmitted by primary users and those transmitted by secondary users.3 Once a jammer has detected signals from secondary users on the channel, it will carry out an attack by jamming the channel for the rest of the time slot. Hence, if the SU transmits real data, its receiver cannot receive signals and thus the SU will waste energy on data 3 Through the sensing process, jammers can detect signals from primary users by using a cyclostationary

feature detection technique as presented in [28, 29].

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transmission. However, if the SU performs a deception by transmitting fake data to the channel, it can entrap jammers into attacking and weaken them while still saving energy for real transmissions. We assume that the SU requires edec su units of energy to perform units of energy to transmit real data. In practice, we a deception, while it requires etran su tran since the SU does not need to process fake data (e.g., by signal < e always have edec su su modulation) and we also can control the transmission time to save energy as illustrated in Figure 10.15. The jammers are equipped with a battery with a capacity of Eja units of energy. Similarly to the SUs, the jammers are also able to harvest energy from the energy har source, and we assume that they can harvest ehar ja units of energy with probability pja at each time slot. At the beginning of each time slot, the jammers perform sensing on the primary channel. If the sensed channel is occupied by SUs and the jammers have enough energy, the jammers will perform attacks by jamming transmission signals. We assume that a jammer has to use eatt ja to perform an attack. Moreover, to guarantee success for the jamming process, the jamming power must be higher than the data transmission power, tran i.e., eatt ja ≥ esu . We assume that there are J jammers and that they can attack SUs by using either independent attacks or coordinated attacks. For the independent attack strategy, the jammers perform attacks individually without communicating with each other, and hence it can happen that there are multiple jammers jamming the same channel concurrently. On the other hand, for the coordinated attack strategy, jammers are assumed to be able to communicate with each other, and thus the attacks by jammers will not overlap. In particular, when there are multiple jammers with enough energy, one of them will be selected randomly to attack the channel. As a result, other jammers can conserve their energy for future attacks. In the following, we will study solutions for SUs to optimize their throughput under attack by jammers. We discuss two scenarios. In the first scenario, we adopt the learning algorithm (discussed in the previous sections) to find the optimal policy for a single SU. Then, in the second scenario, we develop the learning algorithm for the case with multiple SUs that can cooperate to deal with attacks from jammers.

10.4.1

Learning Algorithm for Single Secondary User under Jamming Attacks In this section, we consider the scenario with a single SU that wants to maximize its throughput in a wireless-powered CRN under attack by jammers. First, an MDP framework is used to formulate the throughput optimization problem for the SU. Then, the simulation-based learning algorithm will be adopted to find the optimal policy for the SU.

10.4.1.1

Problem Formulation State Space The state space of the SU can be defined as follows:   S  (e, q); e ∈ {0, 1, . . . , Esu }, and q ∈ {0, 1}, ,

(10.67)

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where e and q express the energy state and the data queue state of the SU, respectively. Without loss of generality, we assume that the queue state has two values, i.e., 0 and 1, corresponding to when the SU has no data and has some data, respectively. For the battery, the energy level is divided into discrete levels and the maximum capacity of the battery is Esu .

Action Space After obtaining sensing results from the primary channel, the SU needs to make a decision. If the sensed channel is busy, the SU will do nothing. However, if the sensed channel is idle, the SU can transmit actual data or perform a deception. Then, the action space of the SU can be defined as follows:   A  a : a ∈ {1, 2, 3} , (10.68) where ⎧ ⎨ 1, a= 2, ⎩ 3,

when the SU does nothing, when the SU performs deception, i.e., transmitting a fake packet, when the SU transmits actual data.

Additionally, the action space given the state of the SU As comprises all possible actions that do not make a transition to a state that is not allowed. Thus, the action space As at the current state s ∈ S is defined as follows: ⎧ if es < edec ⎨ {1}, su , tran As = (10.69) ≤ es < etran {1, 2}, if edec su su OR if esu ≤ es and qs = 0, ⎩ ≤ e and d > 0. {1, 2, 3}, if etran s s su

Transition Probability Function As in Sections 10.2 and 10.3, by using the simulation-based method, for a given control policy , the transition probability function P of the SU can be expressed as follows: $     % P s(t + 1)|s(t),  = P e(t + 1), q(t + 1) | e(t), q(t) ,     Penv p e(t), q(t) p((a(t))), if e(t + 1) = E ∗ and q(t + 1) = Q ∗ , = (10.70) 0, otherwise, where Penv is a probability function of the simulator that generates simulation parameters  for the system process, e.g., parameters of the cognitive radio channel and jammers. p e(t), q(t) is the probability that the SU is at state s at time slot t. p((a(t))) is the probability that the SU takes action a under the control policy  at time slot t. Moreover,       ∗ tr + ∗ Q = min [q(t) − q (t)] + λ(t) , 1 and E = min e(t) − etr (t)]+ + ehar su (t) , Esu . Here, qtr (t) is the number of transmitted packets at time slot t, λ(t) is the number of tr arriving packets, ehar su (t) is the amount of energy harvested, and e (t) is the amount of + energy used at time slot t. Furthermore, [x] = max(x, 0). Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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Reward Function We define the immediate reward function for the SU as the number of packets transmitted as follows:  1, if a packet is successfully transmitted, R(s, a) = (10.71) 0, otherwise.

10.4.1.2

Learning Algorithm As in Sections 10.2 and 10.3, we also adopt the learning algorithm based on the simulation method which will update learning parameters at every time step. The detail of the algorithm is presented in Algorithm 10.5, where κ is a positive constant and ρk is the step size of the algorithm. Algorithm 10.5 Algorithm to update at every time slot  k ) are available from At time slot k, the state is sk , and the values of k , zk , and R( the previous iteration. We update zk , the parameter vector k , and the estimated average k according to reward R  ∇μ k (sk , ak )/μ k (sk , ak ), if sk = s† , zk+1 = (10.72) zk + ∇μ k (sk , ak )/μ k (sk , ak ), otherwise, k )zk+1 , (10.73) k+1 = k + ρk (R(sk , ak ) − R k+1 = R k + κρk (R(sk , ak ) − R k ). R

10.4.2

(10.74)

Optimal Policy for Multiple Secondary Users In this section, we study the case in which there are multiple SUs coexisting in the same environment and they want to cooperate to achieve the best possible performance under attack by jammers. First, we present a centralized learning solution, which can obtain the optimal solution for the whole system, but requires communication among the SUs. Second, we introduce a learning algorithm based on TDMA technique, which can reduce the communication overhead for the SUs.

10.4.2.1

Centralized Learning Solution In the first case, we assume that there exists an access point that operates as a centralized node, i.e., it collects information on the SUs (e.g., data and energy queue states), then processes that information to find the optimal decisions for SUs. After that, decisions are sent to corresponding SUs in order for them to perform the selected tasks.

State Space We assume that there are N cooperative SUs in the network. The state space of SU n is defined in a similar way to (10.67), i.e.,   n }, qn ∈ {0, 1} . (10.75) S n  (en , qn ); en ∈ {0, 1, . . . , Esu Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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At the beginning of each time slot, SUs send information on their local states to the centralized node. Then, the global state space of the whole system can be defined as follows: S cen  (S 1 × · · · × S n × · · · × S N ).

(10.76)

Action Space Similarly, the local action space for SU n can be defined as in (10.68), i.e.,   An  an : an ∈ {1, 2, 3} .

(10.77)

Then, the global action space of the system can be defined as a composite of the local action spaces of all of the SUs as follows: Acen  (A1 × · · · × An × · · · × AN ).

(10.78)

In this section, multiple SUs want to access the channel, but there is only one primary channel to access. Thus, there is a need for the channel access constraint of the global action space such that there is at most one SU accessing the channel, i.e., transmitting data or performing deception, at a time. We then derive the following proposition for the action space constraint of SUs. proposition 10.4. At time slot t, the system is in the state scen = (s1 , . . . , sN ) N 1 and the action space corresponding to the current state is Acen scen = (As1 , . . . , AsN ). Then, we have |Acen scen | =

N 

|Ansn | − N + 1,

(10.79)

n=1

where |Ansn | is the cardinality of the action space An of SU n given the current state sn . The proof of Proposition 10.4 is given in Appendix C in [17]. From Proposition 10.4, when all of the SUs have the action space, i.e., |Ansn | = 3 ∀n ∈ {1, . . . , N}, the bound of the action space of the system is 2N + 1, which significantly reduces the size of the action space.

Transaction Probability Function and Immediate Reward Function Then, the transition probability function and the immediate reward function can be defined in a similar way to in Section 10.4.1, as follows:   P scen (t + 1)|scen (t),  cen % $   = P qcen (t + 1), ecen (t + 1) | qcen (t), ecen (t) ,  cen   ⎧ /N ⎨ psim n=1 p en (t), qn (t) p( cen (an (t))), if en (t + 1) = En∗ = (10.80) and qn (t + 1) = Q∗n , ⎩ 0, otherwise Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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and

 R cen (scen , acen ) =

1, 0,

if a packet is successfully transmitted, otherwise.

(10.81)

Then, as in previous sections, the simulation-based learning algorithm (as presented in Section 10.4.1) can be adopted to find optimal policies for SUs. The details of the learning algorithm are presented in Algorithm 10.6. Algorithm 10.6 The centralized learning algorithm Requirement. Secondary users establish connections to the access point. sys sys sys < ε) do while (R sys (sk , ak ) − R k SUs send their information, i.e., data queue state and energy level, along with sensing results, to the access point. The access point makes decisions on the basis of information received from secondary users and sends the decisions to secondary users. The secondary users perform actions specified by the access point and send the results back to the access point. From the received results, the access point updates the global system values, i.e., sys , according to zsys , sys , and R ⎧ sys sys sys sys sys ⎨ ∇μsyssys (ssys if sk = s† , k , ak )/μ sys (sk , ak ), k sys k zk+1 = (10.82) sys sys sys sys sys sys sys ⎩ zk + ∇μ sys (sk , ak )/μ sys (sk , ak ), otherwise, k

k

sys sys sys sys sys )zsys , k+1 = k + ρk (R sys (sk , ak ) − R k k+1 sys = R sys + κρk (R sys (ssys , asys ) − R sys ). R k+1 k k k k

(10.83) (10.84)

SUs update information on the data queue and energy level on the basis of environment parameters, e.g., arriving packets and energy harvested. end while Algorithm 10.6 will stop when the difference between the average throughput, i.e., sys sys sys , is lower than a preR sys (sk , ak ), and the estimated average throughput, i.e., R k defined threshold, i.e., ε. In other words, Algorithm 10.6 will converge if the condition sys sys sys < ε) is satisfied. (R sys (sk , ak ) − R k

10.4.3

TDMA-Based Learning Solution Learning solutions based on a central node can help us to find the joint optimal policy for SUs, but the communication between SUs and the central node may be expensive since they need to exchange information during every time slot. Furthermore, although, with the proposed constraints, we can limit the action space of the system, the state space is still very large and much impacted by the number of SUs. For example, with four SUs, the state space of the system is (11 × 2)4 = 234,256 states, which is intractable to calculation. Therefore, in this section, we consider a TDMA technique combined with a learning algorithm to solve the existing problems of centralized solutions. There

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are two main reasons for using the TDMA technique. First, TDMA is one of the most common and efficient solutions for multi-access problems in CRNs as well as in other multi-access networks, e.g., WLANs and cellular networks. Second, compared with centralized solutions, by using TDMA, we can avoid the communication overhead and reduce the complexity as well as the curse of dimensionality in state space and action space. With the TDMA technique, we can formulate the optimization problem for SUs and use the learning algorithm as in previous sections. In the formulation, there is just a slight difference in defining the transition probability function for SU n as follows:   P sn (t + 1)|sn (t),  n % $   = P en (t + 1), qn (t + 1) | en (t), qn (t) ,  n ⎧   ⎪ ⎨ (Penv )N p en (t), qn (t) p((an (t))), if en (t + 1) = En∗ (10.85) = and qn (t + 1) = Q∗n , ⎪ ⎩ 0, otherwise. Here, (Penv )N is calculated N times because we have N SUs making decisions regarding accessing the channel in a a round-robin fashion. In particular, during times when SUs are not in decision epochs, they still need update information from the data queue and the energy queue. Then, we can apply a simulation-based learning algorithm similar to that presented in Section 10.4.1 to find optimal policies for SUs. The detail of the TDMA learning algorithm for cooperative SUs in this section is presented in Algorithm 10.7. The proof of convergence of Algorithm 10.7 is similar to the proof of convergence of Algorithm 10.2, which is provided in Appendix B of [15]. Algorithm 10.7 The TDMA learning algorithm Requirement. Each secondary user determines its time sequence number, i.e., the time slot that it is allowed to access the channel in a round-robin fashion. n )zn < ε) do while (R n (snk , ank ) − R k k+1 for n := 1 to N do if SU n is allowed to transmit at time slot t then SU n makes a decision based on the current information and then updates its n as follows: values of zn , n , and R  if snk = s∗n , ∇μn n (snk , ank )/μ nk (snk , ank ), k znk+1 = (10.86) znk + ∇μn n (snk , ank )/μn n (snk , ank ), otherwise, k

nk+1 n R k+1

= =

k

n )zn , nk + ρk (R n (snk , ank ) − R k k+1 n n n n  n ). Rk + κρk (R (sk , ak ) − R k

(10.87) (10.88)

end if SU n updates information on the data queue and energy level on the basis of environment parameters, e.g., arriving packets and energy harvested. end for end while Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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10.4.4

Performance Evaluation

10.4.4.1

Parameter Setting We perform simulations using MATLAB to evaluate the performance of the CRN for different parameter settings and scenarios. First, we consider the scenario with one SU under attack by jammers. Then, in the case with multiple SUs, we vary the number of SUs and the number of jammers, and compare the performance of the proposed TDMA-LA with those of other algorithms, i.e., conventional TDMA, random policy, and a backoff algorithm [31]. • • •

Conventional TDMA. SUs are allowed to access the channel in a round-robin fashion. When an SU is allowed to use the channel, if the channel is idle, it will transmit data as long as it has enough energy and its data queue is not empty. Random policy. When an SU has a packet and enough energy, if the channel is idle, it will select one of two actions, i.e., to transmit data or do nothing, with the same probability of 0.5. Static backoff algorithm. When the channel is idle, an SU will transmit data when it has data and enough energy. If a collision occurs, the SU will choose a backoff counter between 1 and 3 randomly. Then, this backoff counter will be reduced by one. When the backoff counter is equal to zero, the SU will re-transmit the packet.

For the learning algorithm, we set the parameter vector = 0, i.e., the SU will select an action with uniform probability at the beginning of the algorithm. Moreover, parameters for SUs are given in Table 10.3, and parameters for jammers are given in Table 10.4. Table 10.3. Setup parameters for SUs Parameter

Value

Maximum data queue size Maximum energy queue size The packet arrival probability Energy to transmit a packet Energy to perform deception Probability that the SU can harvest one unit of energy each time slot Probability of successful packet transmission by the SU (without jamming) Sensing error probabilities of the SU, i.e., false alarm and missed detection Idle channel probability

1 packets 10 units 0.1 3 units 1 units 0.5 0.95 0.01 0.85

Table 10.4. Setup parameters for jammers Parameter

Value

Maximum energy queue size Energy consumed to perform the attack Probability that the jammer can harvest one unit of energy each time slot

5 units 5 units 0.5

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Figure 10.16 (a) The average throughput and (b) the average delay of the SU, and (c) the average

attacks of jammers, when the energy harvesting probability of the SU and jammers is varied.

Single secondary user: impact of energy harvesting In wireless-powered CRNs, the energy harvesting capacity is one of the most important factors affecting the decisions of jammers and the SU as well as the network performance. Therefore, in the simulation, we vary the energy harvesting probability of the SU together with that of the jammers and evaluate the performance of the system under the average throughput of the SU and the average delay of packets in the data queue. To make fairness evaluations, we assume that the energy capacities of the SU and jammers are the same and we then vary the energy harvesting probability as illustrated in Figure 10.16. As the energy harvesting probability increases, the total amount of energy harvested both by the SU and by the jammers increases, and thus the average number of attacks by jammers increases. However, because of the effectiveness of the deception mechanism, the average throughput of the SU increases, while the average delay will be reduced for the learning algorithm in both cases, i.e., under independent and coordinated attacks. In addition, the performance of the SU obtained by the learning algorithm is much better than that of the greedy policy, especially when the jammers employ coordinated attacks. In particular, in Figure 10.16(a), when the attacks are independent, as the harvesting probability increases from 0.1 to 0.8, the gap between the average throughput of the learning algorithm and that of the greedy policy is also increased. When the energy harvesting probability is 0.8, the average throughput obtained by the learning algorithm is approximately 1.3 times higher than that of the greedy policy. When the energy harvesting probability is 1, the average throughput of both algorithms increases significantly. This is because, when the energy harvesting probability is 1, jammers are able to harvest energy at every time slot. Consequently, they will have the same energy levels as well as decisions when they attack the SU. Thus, the attacks are redundant if jammers independently attack the channel. As a result, the effectiveness of the attack is reduced significantly, which creates favorable conditions for the SU to improve its throughput. Nevertheless, for the coordinated attack strategy of jammers, the effectiveness of the attacks is improved remarkably, especially when the energy harvesting probability is high. Specifically, if the SU uses the greedy policy, the average throughput is approximately zero, i.e., no packet is successfully transmitted. However, under the proposed learning algorithm, even with coordinated attacks, the SU still has opportunities to transmit packets successfully through using the deception strategy. Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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Figure 10.17 Average throughput of the system under (a) independent and (b) coordinated attacks

by jammers when the number of jammers is varied.

Multiple secondary users: impact of the number of secondary users and jammers Now, we study the case in which there are multiple SUs wanting to cooperate to maximize the overall average throughput for the secondary system. We evaluate the performance of the system through the average throughput of SUs when the number of jammers is varied while the number of SUs is fixed at five, as shown in Figure 10.17. As shown in Figure 10.17(a), as the number of jammers increases, the average throughputs of all algorithms are reduced gradually, and the average throughput obtained by the TDMA-LA always achieves the best performance, followed by the conventional TDMA, the random policy, and the backoff algorithm. Here, we observe that the average throughput of the conventional TDMA is quite close to that of the TMDA-LA. The reason is that, when the number of SUs is high, i.e., five in this case, using TDMA can avoid collisions and the SUs have more time to harvest energy. As a result, when an SU is scheduled for transmission, most often it has enough energy to transmit data. Similar results are also observed in Figure 10.17(b) when the jammers perform coordinated attacks. However, in this case, when the number of jammers is large, i.e., double that of SUs, the average throughput of all algorithms is nearly zero since the jammers now can effectively perform attacks in every time slot. Then, we increase the number of SUs while the number of jammers is fixed at five (as shown in Figure 10.18). Here, we observe that the average throughput of the TDMA-LA is still highest, and its performance is patently superior to other algorithms when the jammers use the coordinated strategy as shown in Figure 10.18(b). Here, differently from TDMA-based techniques, the average throughput obtained by the random policy and the static backoff algorithm decreases when the number of SUs is greater than five because there will be more collisions among SUs, resulting in a low network throughput. Here, we also consider the result obtained using the centralized learning algorithm, i.e., Algorithm 10.6, when the number of SUs is two. The reason is Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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Figure 10.18 Average throughput of the system under (a) independent and (b) coordinated attack

by jammers when the number of secondary users is varied.

that, when the number of secondary users is greater than two, we are unable to use the centralized solution since the state space is too large. When the number of secondary users is two, we can observe that the average throughput obtained by the TDMA-LA is quite close to the result obtained by the centralized learning algorithm. The main reason is that we have only one channel and thus the TMDA-LA can achieve a high performance in our proposed system. In summary, we make two important observations as follows. •

•

10.5

In the case with one SU, the learning algorithm (i.e., Algorithm 10.5) yields much better performance than that of the greedy policy. Additionally, with the learning algorithm, the SU can automatically and adaptively adjust its strategy according to different strategies of jammers and the dynamics of the cognitive radio environment. In the case with more than one SU, the TDMA-LA yields results close to those obtained by the centralized learning algorithm. Moreover, the results obtained by the TDMA-LA are much better than those of other algorithms, i.e., conventional TDMA, random policy, and a backoff algorithm for different numbers and strategies of jammers.

Future Research Directions There are some research directions relating to this topic deserving study. •

Game theory and applications in energy harvesting CRNs. In this chapter, though many problems concerning energy harvesting CRNs have been discussed, most of them are optimization problems, e.g., minimizing delay and maximizing throughput or performance. However, in practice, wireless nodes are not always willing

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10.6

to cooperate and thus we need adopt game theory in analyzing the competition relation among them. In addition, game models can support distributed decision making by using local information and thus wireless nodes can avoid communication overhead and minimize energy consumption. For example, by applying repeated games [32] with punishment mechanisms, we can encourage wireless nodes to cooperate in a distributed way and avoid network disruption due to selfish behaviors. Integrating energy harvesting CRNs with other networks. With the many advantages presented in this chapter, energy harvesting CRNs have become more and more popular and they can be integrated into many other networks, e.g., the Internet-of-Things (IoT), body area networks, and machine-to-machine communications, to enhance performance efficiency. For example, sensors/actuators in IoT have to gather and transmit data to the central node for further processing. In order to reduce human intervention while still guaranteeing quality-of-service for IoT, sensors/actuators must be “smarter.” In particular, they should be able not only to harvest energy to serve for their operation, but also to choose efficient channels to transmit data. Therefore, it is clear that the advantages of energy harvesting CRNs will bring many benefits for the development of other networks in the near future. Design and implement on hardware devices. Most of the current research has focused on developing applications of energy harvesting CRNs, while the question of how to design and implement such applications in practice has not received sufficient attention. The implementation of energy harvesting circuits along with transceivers on the same device can cause negative impacts for the device, e.g., it can reduce the energy harvesting capability and data transmission performance. However, there is still a lack of research work investigating the implementation problem for wireless nodes in energy harvesting CRNs. Therefore, this is an important step that needs to be taken into account before energy harvesting CRNs can be implemented in practice.

Summary The development of wireless energy harvesting techniques has brought many advantages for cognitive radio networks (CRNs). In particular, in wireless energy harvesting CRNs, cognitive users are able not only to opportunistically access available spectrum, but also to automatically harvest energy to prolong the operation time without human intervention. In addition, with the implementation of wireless energy harvesting techniques in CRNs, we can reduce a significant cost in suppling power for wireless nodes by scavenging natural energy sources, e.g., ambient signals. In this chapter, we first discussed applications of energy harvesting techniques in many scenarios in CRNs. Then, we introduced an optimization framework for using RF energy harvesting in CRNs and presented some optimization solutions for secondary users such that they can maximize their overall throughput. We also introduced a scenario with attacks by jammers in such an environment and discussed some approaches to cope with this

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problem. Simulation results demonstrated the efficiency of the proposed solutions as well as the potential benefits of harvesting wireless energy for CRNs. Finally, we also highlighted some future research directions in this topic.

References [1] FCC, ET Docket No 03-322 Notice of Proposed Rule Making and Order, December 2003. [2] S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE Journal on Selected Areas in Communications, vol. 23, no. 2, pp. 201–220, February 2005. [3] Q. Zhang, B. Cao, Y. Wang et al., “On exploiting polarization for energy-harvesting enabled cooperative cognitive radio networking,” IEEE Wireless Communications, vol. 20, no. 4, pp. 116–124, August 2013. [4] A. Sultan, “Sensing and transmit energy optimization for an energy harvesting cognitive radio,” IEEE Wireless Communications Letters, vol. 1, no. 5, pp. 500–503, October 2012. [5] X. Gao, W. Xu, S. Li, and J. Lin, “An online energy allocation strategy for energy harvesting cognitive radio systems,” in International Conference on Wireless Communications & Signal Processing (WCSP), October 2013, pp. 1–5. [6] S. Park, H. Kim, and D. Hong, “Cognitive radio networks with energy harvesting,” IEEE Transactions on Wireless Communications, vol. 12, no. 3, pp. 1386–1397, March 2013. [7] N. Barroca, J. M. Ferro, L. M. Borges, J. Tavares, and F. J. Velez, “Electromagnetic energy harvesting for wireless body area networks with cognitive radio capabilities,” in Proc. URSI Seminar of the Portuguese Communications, Lisbon, Portugal, November 2012. [8] S. Lee, R. Zhang, and K. Huang, “Opportunistic wireless energy harvesting in cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 9, pp. 4788–4799, September 2013. [9] J. F. C. Kingman, Poisson Processes. Oxford: Oxford University Press, 1993. [10] X. Lu, W. Xu, S. Li, J. Lin, and Z. He, “Simultaneous information and power transfer for relay-assisted cognitive radio networks,” in International Conference on Communications Workshops, pp. 331–336, Sydney, Australia, June 2014. [11] Z. Wang, Z. Chen, Y. Yao, B. Xia, and H. Liu, “Wireless energy harvesting and information transfer in cognitive two-way relay networks, in “IEEE Global Communications Conference, Austin, TX, December 2014, pp. 3465–3470. [12] A. H. Sakr and E. Hossain, “Cognitive and energy harvesting-based D2D communication in cellular networks: Stochastic geometry modeling and analysis,” IEEE Transactions on Communications, pp. 1867–1880, vol. 63, no. 5, May 2015. [13] S. Park, J. Heo, B. Kim, and W. Chung, “Optimal mode selection for cognitive radio sensor networks with RF energy harvesting,” in Proc. IEEE International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), September 2012. [14] S. Park and D. Hong, “Optimal spectrum access for energy harvesting cognitive radio networks,” IEEE Transactions on Wireless Communications, vol. 12, no. 12, pp. 6166–6179, December 2013. [15] D. T. Hoang, D. Niyato, P. Wang, and D. I. Kim, “Opportunistic channel access and RF energy harvesting in cognitive radio networks,” IEEE Journal of Selected Areas in Communications, vol. 32, no. 11, pp. 2039–2052, November 2014. Downloaded from https:/www.cambridge.org/core. The Librarian-Seeley Historical Library, on 27 Jan 2017 at 15:42:43, subject to the Cambridge Core terms of use, available at .011

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[16] D. T. Hoang, D. Niyato, P. Wang, and D. I. Kim, “Performance optimization for cooperative multiuser cognitive radio networks with RF energy harvesting capability,” IEEE Transactions on Wireless Communications, vol. 14, no. 7, pp. 3614–3629, July 2015. [17] D. T. Hoang, D. Niyato, P. Wang, and D. I. Kim, “Performance analysis of wireless energy harvesting cognitive radio networks under smart jamming attacks,” IEEE Transactions on Cognitive Communications and Networking, vol. 1, no. 2, pp. 200–216, February 2015. [18] D. Niyato, P. Wang, and D. I. Kim, “Channel selection in cognitive radio networks with opportunistic RF energy harvesting,” in IEEE International Conference on Communications, Sydney, Australia, June 2014, pp. 1555–1560. [19] M. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming. Hoboken, NJ: Wiley, 1994. [20] A. Gosavi, Simulation-Based Optimization: Parametric Optimization Techniques and Reinforcement Learning. Berlin: Springer, 2003. [21] O. Buffet, A. Dutech, and F. Charpillet, “Shaping multi-agent systems with gradient reinforcement learning,” Journal of Autonomous Agents and Multi-Agent Systems, vol. 15, no. 1, pp. 197–220, January 2007. [22] P. Marbach and J. N. Tsitsiklis, “Simulation-based optimization of Markov reward processes,” in IEEE Transactions on Automatic Control, vol. 46, no. 2, pp. 191–209, February 2001. [23] J. Baxter, P. L. Barlett, and L. Weaver, “Experiments with infinite-horizon, policy-gradient estimation,” Journal of Artificial Intelligence Research, vol. 15, no. 11, pp. 351–381, November 2001. [24] Dimitri P. Bertsekas, Nonlinear Programming. Belmont, MA: Athena Scientific, 1995. [25] D. Bernstein, R. Givan, N. Immerman, and S. Zilberstein, “The complexity of decentralized control of Markov decision processes,” Journal of Mathematics of Operations Research, vol. 27, no. 11, pp. 819–840, November 2002. [26] H. W. Kuhn and A. W. Tucker, “Nonlinear Programming,” in Proc. 2nd Berkeley Symposium on Mathematical Statics and Probability, 1951, pp. 481–492. [27] V. S. Borkar, Stochastic Approximation: A Dynamic Viewpoint. Cambridge: Cambridge University Press, 2008. [28] E. Hossain, D. Niyato, and Z. Han, Dynamic Spectrum Access and Management in Cognitive Radio Networks. Cambridge: Cambridge University Press, 2009. [29] Y. Liu, P. Ning, and H. Dai, “Authenticating primary users’ signals in cognitive radio networks via integrated cryptographic and wireless link signatures,” in IEEE Symposium on Security and Privacy, Oakland, MD, May 2010, pp. 286–301. [30] K. Pelechrinis, M. Iliofotou, and S. V. Krishnamurthy, “Denial of service attacks in wireless networks: The case of jammers,” IEEE Communications Surveys and Tutorials, vol. 13, no. 2, pp. 245–257, May 2011. [31] D. T. Hoang and D. Niyato, “Performance analysis for cognitive machine-to-machine communications”, in IEEE International Conference on Communication Systems (ICCS), Singapore, November 2012, pp. 245–249. [32] D. T. Hoang, X. Lu, D. Niyato et al., “Applications of repeated games in wireless networks: A survey,” IEEE Communications Surveys and Tutorials, vol. 17, no. 4, pp. 2102–2135, April 2015.

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11

Mobile Ad-Hoc Networks and Delay-Tolerant Networks With Wireless Energy Harvesting Dusit Niyato

11.1

Introduction Mobile ad-hoc Networks (MANETs) are composed of mobile nodes communicating over multiple hops from a source to a destination. They do not have an infrastructure such as a base station or an access point to facilitate data transfer. Mobile nodes acting as relays receive data from the source or other relays and forward such data to the next hop until the destination has been reached. Delay-tolerant Networks (DTNs) are a special kind of MANET that will allow mobile nodes to receive, store, and forward data when they move and meet each other. Unlike in MANETs, in DTNs, there is no need for an end-to-end path from the source to the destination when the data are transferred. Thus, DTNs are suitable for non-real-time traffic, namely delay-tolerant traffic. Typically, in MANETs and DTNs, the energy supply to the mobile nodes in the networks is limited and intermittent. Additionally, mobility makes data transfer less reliable than in infrastructure-based wireless networks such as cellular systems. Therefore, when one adopts wireless energy harvesting and transfer, some related issues, e.g., routing and energy replenishment, have to be revisited. This chapter deals with wireless-powered MANETs and DTNs. Firstly, overviews of MANETs and DTNs are presented. Some issues related to energy in conventional MANETs and DTNs are discussed. Then, the chapter presents in detail energy management approaches for mobile nodes in wireless-powered MANETs and DTNs. •

The first approach deals with content delivery services in a wireless-powered DTN. In the network, a mobile node acting as a mobile router moves randomly to collect content from a content source and deliver it to a gateway. The mobile node receives energy from the gateway, and thus must optimize energy usage for content delivery. A constrained Markov decision process (CMDP) is formulated and solved to obtain an optimal content delivery policy. Additionally, multiple mobile nodes can help each other to deliver content from different content

Wireless-Powered Communication Networks: Architecture, Protocols, and Applications, ed. Dusit Niyato, Ekram Hossain, Dong In Kim, Vijay Bhargava, and Lotfollah Shafai. Published by Cambridge University Press. © Cambridge University Press 2017.

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sources. A coalition formation game is applied to determine an optimal coalition among mobile nodes. The second approach considers delay-limited communication in the wirelesspowered MANET. The mobile node generates and has to transmit delay-sensitive data before a deadline. If the deadline is violated, the data become useless and will be discarded and lost. Since the mobility of the mobile node is random, its energy supply is intermittent. The mobile node has to optimize its delaysensitive data transmission. A CMDP is formulated and solved to obtain the transmission policy. Additionally, the energy management of a wireless charger to transfer energy to multiple mobile nodes is considered. A simple thresholdbased scheme is introduced and its performance is analyzed in order to obtain an optimal threshold. Then, the optimal deployment of multiple wireless chargers at different locations is studied in order to minimize the total cost in terms of the deployment and energy consumption cost. The third approach studies mobile energy sharing in a wireless-powered DTN. In the network, mobile nodes not only transfer content for each other, but also share their energy to minimize the chance of an energy outage event. Consider two mobile nodes matched to share energy. First the CMDP is used to obtain an optimal energy sharing policy. For example, the mobile node with a higher energy level in its battery should transfer energy to the mobile node with a lower energy level. In the optimal energy sharing policy, the mobile nodes aim to match with each other so that their performance is maximized, i.e., their energy outage probability is minimized. The stable matching structure is obtained as the solution.

Finally, some future research directions are discussed. For example, mobile nodes can explore other mechanisms for controlling energy supply, including auction and contract theory.

11.2

Basics of MANETs and DTNs

11.2.1

Mobile Ad-Hoc Networks (MANETs) MANETs originated from the mobile packet radio networking used in military applications. In MANETs, mobile nodes communicate with each other over wireless links without using a fixed infrastructure. A mobile node as a source transfers data via relays to the destination. Figure 11.1 shows an example of a MANET. Node A transfers data to node D over relay nodes B and C. The topology of the network can change dynamically because of users’ mobility, e.g., some nodes arrive and some other nodes leave the network. Thus, the mobile nodes must have the ability to adapt to the random and unpredictable network conditions and organize themselves to provide functionality and achieve the goal of the network. Because of the lack of a network infrastructure and a centralized controller, mobile nodes have to maintain the network, perform routing, and carry out management autonomously in a distributed fashion. This introduces more complexity to the network, while the resources in terms of available bandwidth and energy are still limited. 10 Mar 2017 at 08:08:03, .012

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Figure 11.1 An example of a mobile ad-hoc networks (MANET).

One of the major issues in MANETs is routing. Since the topology of the network constantly changes, mobile nodes in the networks must be able to maintain and find an optimal route from the source to the destination in an optimal way [1]. The routing protocols for MANETs must be designed in a distributed fashion because there is no centralized controller to maintain a global network status and routing table. The routing protocols must ensure that there is no loop in the path to be used, in order to avoid bandwidth and energy wastage. Moreover, the routing protocols should be able to support MAC protocols to reduce energy consumption. Routing protocols in MANETs can be broadly classified into two types, i.e., proactive and on-demand routing. •

•

In proactive routing, the protocols maintain a routing table to reach destinations in the network. The mobile nodes periodically disseminate and exchange the routing table among each other in order to have the latest information on the network. Some examples of proactive routing protocols are the optimized link state routing (OLSR) protocol and the destination sequence distance vector (DSDV). When mobile nodes have data to transmit, they can retrieve an optimal route from their pre-determined routing table with minimal latency. However, because of the need for periodic exchange of routing information, proactive routing can cause a considerable amount of overhead. Moreover, if the network mobility is high, i.e., the topology changes quickly, proactive routing may fail to adapt and maintain up-to-date routing information. In on-demand routing, routing information will be acquired only when a mobile node has data to transmit. This can be done by typically flooding the network with route request messages. Once the destination has received the message, it will reply with information about an optimal route. Some examples of on-demand routing protocols are ad-hoc on-demand distance vector (AODV) and dynamic source routing (DSR). In on-demand routing, there is no exchange of routing information if there are no data to transmit. Thus, its overhead is usually less than that of proactive routing. However, on-demand routing protocols may suffer from high delay incurred in finding the best route when a mobile node has data to transmit. Furthermore, because of route request flooding, network congestion may easily happen when many mobile nodes have data to transmit at the same time. 10 Mar 2017 at 08:08:03, .012

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In addition to proactive and on-demand routing, MANETs can use hybrid protocols that combine their advantages to improve routing performance. In hybrid routing, mobile nodes maintain some routing information of the network by proactively exchanging routing information periodically. When a mobile node has data to transmit, it chooses to use the information from the table to transmit the data. Alternatively, it can choose to send a route request message on a set of selected paths from the available proactive routing information. In this way, the latency of data transmission and overhead due to periodic exchange of routing information can be reduced. An example of the hybrid routing is the zone routing protocol (ZRP). Proactive, on-demand, and hybrid routing rely on a flat structure of the network, namely that all mobile nodes have the same functionality to relay data for each other. Alternatively, MANETs can be organized with a hierarchical structure. In this case, mobile nodes are classified as part of the network at different levels in the hierarchy. Routing and data transfer will be performed according to the levels of hierarchy. One example of hierarchical routing is the cluster-based routing protocol (CBRP). In this protocol, the mobile nodes are divided into cluster members or cluster heads. A cluster member will first transmit its data to the cluster head of the cluster to which it belongs. Then, the cluster head forwards the data to another cluster head until the data have reached the cluster to which the destination belongs. The benefit of this hierarchical routing is that there is minimal message flooding and high efficiency because only cluster heads perform routing. Energy is the important resource for MANETs. Energy is used mainly for data transmission and reception by a wireless interface of a battery-powered mobile node. Since the mobile node can receive data correctly only if the signal-to-noise ratio (SNR) is maintained above a certain threshold, the energy consumption depends mainly on the distance between the transmitter and receiver. To use energy efficiently, typically the transmitter will be able to adjust the transmit power so that the receive power at the receiver is high enough. Additionally, the wireless interface of the mobile node can operate in different modes, i.e., transmit, receive, idle, and sleep, the energy consumption of which is different. The least amount of energy is consumed in sleep mode. The mobile node consumes the largest amount of energy when it is transmitting data, and a lower amount for receiving data, and being idle. Since energy is an important resource and becomes a crucial parameter, in addition to conventional metrics such as the hop count, routing protocols have to take energy consumption and energy efficiency into account. Conventional routing algorithms for MANETs aim to obtain the route with the least number of hops and ignore the energy supply available to the nodes. Thus, in many cases, bottleneck nodes can deplete their energy quickly and the network can become disconnected. Thus, power-aware routing protocols have been proposed in order to take energy consumption and supply into account. Power-aware routing protocols can be broadly classified into two types, i.e., activitybased and connectivity-based [2]. •

Activity-based power-aware routing. The protocols in this type aim to control an activity, i.e., data transmission, of the mobile nodes in such a way as to reduce energy consumption. One typical approach is to adjust the transmit power for 10 Mar 2017 at 08:08:03, .012

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routing. For example, in unicast transmission, the authors of [3] introduce a new routing cost/metric that takes the residual energy in a battery and the transmit power required to reach other neighbors of mobile nodes into account. The poweraware routing algorithm is proposed to minimize this routing cost, which is shown to be able to extend the network lifetime of each node. Another example is the location-aided power-aware routing (LAPAR) protocol [4], which assumes that the mobile nodes know their own geographical locations. A source mobile node defines a relay region and chooses the region which consumes the least energy. The region includes a set of relay nodes to the destination that reduce energy consumption in comparison with sending directly to the destination. The routing is based on a greedy algorithm that aims to reach a destination by choosing the region with the smallest energy consumption at each hop. The routing decision is made locally without global information on the network. Connectivity-based power-aware routing. The protocols in this type aim to optimize connectivity in the networks so that energy consumption is minimized and the network lifetime is maximized. The connectivity can be adjusted by varying the transmit power. When the transmit power increases, the transmission range increases and the mobile node has more connectivity, i.e., more neighbors. However, this will increase energy consumption and the incidence of transmission collision. Therefore, there is an optimal connectivity of the network that minimizes energy consumption. For example, the authors of [5] introduce a topology control algorithm based on adjusting the transmit power. This algorithm is based on a constrained optimization. The objective is to minimize the maximum power used to establish connectivity with the constraints on necessary connectivity that must be provided to meet data routing requirements. A centralized algorithm is used to obtain an optimal solution, while a distributed heuristic algorithm is introduced to obtain a near-optimal solution without complete information on the network.

Although power-aware routing protocols have been well studied, the energy management for the mobile nodes in MANETs with intermittent energy supply from wireless energy transfer imposes new and unique challenges that need alternative solutions.

11.2.2

Delay-Tolerant Networks (DTNs) DTNs are similar to MANETs in that data transfer is performed among mobile nodes directly without help from infrastructure and centralized controllers. However, in DTNs, there may be no end-to-end path from a source to a destination at the time when the data is transmitted, i.e., there is a lack of continuous network connectivity. Therefore, data transfer is done when mobile nodes move and meet each other. A mobile node, after having received the data, will store them in the data storage. When the node moves and meets another node, it decides whether to transfer the data. With this kind of data transfer, DTNs are suitable for sparse networks, e.g., networks in space. A DTN can be also called a disruption-tolerant network in that it can be used to transfer data even with 10 Mar 2017 at 08:08:03, .012

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Figure 11.2 An example of DTN.

network disruption or with an interruption of connectivity. It can support data transfer among mobile nodes with limited wireless transmission range and energy resources, under cyber and physical attack, and in the presence of noise. Figure 11.2 shows an example of a DTN. Node A is the source. It moves and encounters node B. During the meeting with node B, node A transfers data to node B. Subsequently, after node B has moved and encountered node C, which is the destination, the data are transferred. Owing to the lack of end-to-end connectivity from source to destination, typical wireless routing protocols such as those developed for MANETs cannot be applied. Therefore, a typical routing approach for DTNs is based on data replication and a storeand-forward method. In this approach, data are incrementally received, stored, and forwarded among mobile nodes throughout the networks. This is similar to flooding that maximizes the chance of reaching the destination. The data replication among the nodes must be designed to maximize the probability of successfully reaching the destination. Thus, DTNs require abundant resources in terms of bandwidth, data storage capability, and the number of intermediate nodes. Without global network knowledge and complete information on routing, the data transfer latency in DTNs is expected to be high. Traditionally, this limits the applications of DTNs. Nonetheless, recently DTNs have been applied as an underlying technology for mobile social networks (MSNs) [6] in which data transfer can explore and exploit social relationships among mobile users to optimize the store-and-forward mechanism. Additionally, it is suitable for transferring data packets of with large size, which cannot be done efficiently over broadband connections such as cellular networks. The authors of [7] introduce optimal energy-aware epidemic routing for DTNs. The epidemic routing works by allowing mobile nodes to transfer data when they meet each other. The proposed routing algorithm determines whether a mobile node should transfer data upon contacting a new node. This decision takes the available energy of the mobile nodes and the age of the data into account. The tradeoff between energy conservation and a quality-of-service (QoS) measure is analyzed, whereby the authors formulate an optimal control problem and its optimal solution is obtained to determine the probability of data forwarding. The authors of [8] extend the protocol BUBBLE Rap [9] by incorporating energy parameters. In BUBBLE Rap, the social metrics, i.e., centrality and community, are used as parameters to forward data from one node to another node when they contact each other. The social metrics can be determined from mobility traces or annotated by users. Firstly, mobile nodes are classified into a community. Each node determines a global ranking, which is the global centrality, to determine 10 Mar 2017 at 08:08:03, .012

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the possibility of contact with other nodes in a different community. The node also has a local ranking, which is the local centrality, to determine the possibility of contact with other nodes in a same community. When two nodes meet, they use a utility function to decide whether the data should be forwarded or not. The decision is composed of the global and local ranks of two meeting nodes. For energy-aware BUBBLE Rap, the utility function is also defined according to the residual energy of the mobile nodes. If the available energy is not sufficient to carry and forward the data, the utility will be small. Thus, the probability that the node will forward the data will also be small. The authors of [10] propose an energy management scheme for DTNs, i.e., asynchronous clock-based power saving protocols. The protocols control an energy saving mode, i.e., sleep schedule, of the mobile node. When the mobile node is in a sleep mode, it cannot communicate with other nodes within contact range. Therefore, if the node is in sleep mode frequently, its connectivity will be low. The proposed protocols aim to achieve a tradeoff and optimize this operation. Again, similarly to MANETs, the energy supply is not taken into account when designing energy management or routing protocols. Especially in DTNs, energy supply becomes opportunistic and has to be optimized jointly with data transfer to achieve optimal performance.

11.3

Cooperation in DTNs In DTNs, mobile nodes transfer content from one node to another by mean of mobility. Mobile nodes visiting content sources, e.g., remote sensors, can receive content and deliver it to a gateway. Each mobile node then receives energy, e.g., through wireless charging, from a gateway after the content has been delivered. An example scenario of the wireless-powered DTN is shown in Figure 11.3. In this example, there are three mobile nodes, each of which is associated with a content source and a gateway. That is, one mobile node is to receive content from an associated content source and upload the content to a designated gateway. In this wireless-powered DTN, we study two major issues [12]. 1.

2.

When a mobile node is at a content source, it has to decide whether to receive the content or not. Similarly, when it is at a gateway, it will decide whether to transfer the content, if any, or to receive wireless energy. Since the energy and buffer space are limited, the mobile node has to make the decisions in such a way that their utility is maximized. For example, the node cannot arbitrarily accept all content from the source since this consumes energy and buffer space. Moreover, it has to balance between receiving energy and uploading the content. When there are multiple mobile nodes, they can cooperate and form coalitions to help each other to deliver content from the content sources. In this case, one mobile node can help another node to receive content from a different content source and deliver it to a gateway. Again, the mobile node has to trade off the energy consumption and buffer space of helping other nodes with the benefit 10 Mar 2017 at 08:08:03, .012

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Figure 11.3 Cooperation in wireless-powered DTNs.

gained from the other node helping it. Reciprocal content delivery among multiple nodes can be sustainable if all mobile nodes gain utilities higher than those they would achieve by acting alone. To analyze the above issues, the authors of [12] introduce a performance analysis and optimization framework, which is composed of an optimization and game-theoretic models developed jointly to achieve the goal of the wireless-powered DTN. 1.

2.

The framework introduces an optimization model based on a CMDP for each individual mobile node. The CMDP is used to obtain an optimal content delivery and energy charging policy. In particular, given the state of the mobile node, it takes an action to receive content from the content source or not, and an action to receive energy to upload the content. The constraint on the content blocking is imposed to ensure QoS to the content source. The framework proposes a coalition formation game to analyze the cooperation evolution of the mobile nodes to help each other deliver content given their optimal content delivery and energy charging policy. The goal is to obtain stable coalitions among mobile nodes such that they cannot gain higher long-term utility by changing the coalition.

In this framework, these optimization and game models are interrelated as shown in Figure 11.4. At the higher level, the cooperation among mobile nodes is formulated as a coalition formation game. At the lower level, content delivery and energy charging are formulated as a CMDP optimization. While the coalition formation game yields the 10 Mar 2017 at 08:08:03, .012

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Cooperation among mobile nodes (coalition formation game) Delivery rate (payoff)

Coalition S

Delivery policy optimization (constrained Markov decision process) Figure 11.4 An optimization and game framework for the wireless-powered DTN.

coalition among mobile nodes, the CMDP optimization uses the coalition to optimize the policy. In the literature, buffer management of mobile nodes has been studied [13–24]. For example, the authors of [23] analyzed the message delivery performance and optimized the message forwarding strategies of a number of mobile nodes and traffic sources. In this work, each traffic source can individually control its transmission rate while ensuring that the buffer at the mobile nodes is not overwhelmed, thus improving overall network performance. However, the traffic sources are assumed to be rational. Therefore, a non-cooperative game model is developed to obtain the Nash equilibrium of the transmission rate of the traffic sources. Cooperation between mobile nodes was studied in [24] via a coalition formation game model. Moreover, the energy efficiency of DTNs has been analyzed [25–28]. For example, the authors of [25] derive the network capacity region of the DTN given energy constraints on the mobile nodes. The authors of [26] aim to optimize the duty cycle of the mobile nodes in a DTN. The optimization considers the fact that multiple mobile nodes can form a cluster so that they can coordinate the operations, i.e., switch between active and standby modes to reduce energy consumption. However, no existing work seems to have considered the optimal content delivery and energy charging policy based on the energy state of a mobile node.

11.3.1

System Model In a single-hop wireless-powered DTN, a mobile node acts as a content router to receive content from a content source, move, and deliver it to a gateway, i.e., a content destination. This is similar to a homing-pigeon-based DTN or message ferry DTN, in which the content is not transferred among mobile nodes. Each mobile node is associated with a particular content source and gateway. For example, mobile node i is associated with content source Si and gateway Gi . The mobile node has an energy storage device, i.e., a battery, with Bi units of energy, and a content buffer with a maximum capacity of Qi . The mobile node can take the following actions depending on its location. •

At a content source. The mobile node has to decide whether to accept content from the content source or not. If it receives content, it will consume Jˆ i 10 Mar 2017 at 08:08:03, .012

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Figure 11.5 System model of wireless-powered DTN.

•

units of energy from its battery. We assume that, when mobile node i is at the content source Si , the content source has content to transfer to the mobile node with probability αi . The content is transferred successfully with probability μˆ i . At a gateway. We assume that the mobile node cannot upload content and receive energy at the same time. This could be so because they use the same frequency band when RF energy transfer techniques are adopted. Thus, the mobile node has to decide whether to transfer content if its content queue is not empty or to request and receive energy from the gateway. If the mobile node uploads the content, it will consume Ji units of energy from its battery. The content will be successfully uploaded with probability μi . By contrast, if the mobile node requests energy transfer, it can receive Ki units of energy.

The system model of the aforementioned single-hop wireless-powered DTN is shown in Figure 11.5. In addition to letting a single mobile node transfer content from a content source to a gateway, it is possible that multiple mobile nodes can cooperate and help each other to transfer content from multiple sources to different gateways. In this case, the cooperative mobile nodes have to share the space in their content queues and energy in their energy storage devices. Therefore, the mobile nodes have to decide whether to cooperate and, if so, with which mobile nodes to cooperate. Let N denote the set of mobile nodes, where N = |N | is the total number of all mobile nodes. The mobile nodes can form a cluster of cooperation, which is a subset of N . They will be in a cluster if they have mutual benefits in terms of higher content delivery rate. We model the mobility of a mobile node as a Markov chain. The mobile node visits a location from a finite set. The sets of locations are LS and LG , which are the sets of all locations of content sources and gateways, respectively. The set of all locations is denoted by L = LS ∪ LG . For mobile node i, its probability of moving from loca(i) tion l to location l is given and denoted by ml,l . The transition matrix of mobility is denoted by M(i) , whose elements are m(i) l,l . We denote li ∈ LS as a location with content source Si . 10 Mar 2017 at 08:08:03, .012

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393

Wireless Energy Transfer and Content Transfer Policy We formulate a CMDP to obtain an optimal policy for wireless energy and content transfer. The optimization is for a tagged mobile node that is in a coalition S. The state space of the mobile node is as follows:   = (L , B, Q); L ∈ L, B ∈ {0, 1, . . . , B}, Q ∈ {0, 1, . . . , Q} , (11.1) where L represents the location of a mobile node, B represents the energy level of the energy storage, and Q represents the number of items of content in the content queue of the mobile node. B is the maximum capacity of the energy storage, and Q is the maximum content queue size of the mobile node. We define a composite variable θ = (l, b, q) ∈ , where l, b, and q are the location, energy level, and number of items of content in the content queue, respectively. The action space of a mobile node can be defined as  = {0, 1, 2, 3}, where the meanings of the numbers are • • • •

0, the mobile node does nothing; 1, the mobile node requests wireless energy transfer from the gateway; 2, the mobile node transmits content to the gateway; and 3, the mobile node receives content from the content source.

The objective of the mobile node is to maximize the content delivery rate, while meeting the content blocking probability. Here, the content is blocked if the mobile node refuses to accept content from the corresponding source. The CMDP optimization of the mobile node can be expressed as follows: max JR (π ) π

subject to JL,i (π ) ≤ Li ,

i ∈ S,

(11.2)

where JR (π ) is the steady-state content delivery rate of the mobile node, and JL,i (π ) is the content blocking probability of source Si that is in the same coalition as the mobile node, i.e., i ∈ S. π is the content delivery policy of the mobile node, and Li is the content blocking probability threshold for source i that must be guaranteed by mobile node i. The steady-state content delivery rate and the blocking probability can be defined as follows: 1 E (R(θt , ωt )) , t 

(11.3)

1 t

(11.4)

t

JR = lim inf t→∞

JL,i = lim sup t→∞

t =1 t 

E (Li (θt , ωt )) ,

t =1

where θt ∈ is the state variable, and ωt ∈  is the action variable, for the mobile node at time t . R(·) is the immediate content delivery rate, and Li (·) is the immediate content blocking probability. 10 Mar 2017 at 08:08:03, .012

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The immediate content delivery rate is given as follows:  μ, l ∈ LG , q > 0, b ≥ J, and ω = 2, R(θ, ω) = 0, otherwise,

(11.5)

where θ = (l, b, q) is a composite state variable. In (11.5), the immediate content delivery rate is the successful content transmission probability meeting all the following conditions. • • • •

The mobile node is associated with any gateway (i.e., l ∈ LG ). Its content queue is not empty (i.e., q > 0). The energy level in the energy storage device is larger than or equal to the amount required for uploading content (i.e., b ≥ J). The mobile node decides to upload the content (i.e., ω = 2). The immediate content blocking probability is defined as follows:  1, l = i and b < Jˆ or q = Q or ω = 3, Li (θ, ω) = 0, otherwise.

(11.6)

Content is blocked if a mobile node is with the content source i , and one of the following occurs. • • •

This mobile node does not have enough energy in its storage device to receive content (i.e., b < Jˆ ). Its content queue is full (i.e., q = Q). The mobile node decides not to receive the content (i.e., ω = 3).

To solve for an optimal content delivery policy, we apply a linear programming approach [29]. The optimal randomized policy is denoted by π ∗ (θ, ω) for θ ∈ and ω ∈ . The randomized policy determines the probability of taking action ω when the current state of the mobile node is θ . For the linear programming, φ(θ , ω) is the steady state probability of state θ and action ω. The linear programming model is then expressed as follows:  φ(θ , ω)R(θ, ω), (11.7) max φ(θ ,ω)

θ ∈ ω∈

which is to maximize the content delivery rate, subject to  φ(θ , ω)Li (θ, ω) ≤ Li , i ∈ S,

(11.8)

θ∈ ω∈

which is to guarantee the content blocking probability below a desired threshold,   φ(θ  , ω) = φ(θ , ω)Pθ ,θ  (ω), θ  ∈ , (11.9) ω∈

θ∈ ω∈

which is to satisfy the Chapman–Kolmogorov equation, and  φ(θ , ω) = 1, φ(θ , ω) ≥ 0, θ∈ ω∈

10 Mar 2017 at 08:08:03, .012

(11.10)

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which is to meet the basic probability properties. A standard linear programming solver can be applied to obtain the solution φ ∗ (θ, ω) of the problem in (11.55). The optimal randomized policy of the mobile node can be derived from the optimal solution of the linear programming model, i.e., φ ∗ (θ, ω), as follows: π ∗ (θ, ω) = 

φ ∗ (θ, ω) , ∗  ω ∈ φ (θ, ω )

(11.11)

  for θ ∈ and ω ∈ φ ∗ (θ, ω ) > 0. If ω ∈ φ ∗ (θ, ω ) = 0, then π ∗ (θ, 0) = 1 (i.e., the mobile node will do nothing). With the optimal randomized policy of the mobile node, we can determine the content delivery rate. This is the number of items of content successfully delivered to the corresponding gateway per unit time. We assume that the mobile node always keeps the content after receiving it from the content source until the content is uploaded successfully to the gateway. The content delivery rate of a source i serviced by a mobile node i is the rate at which mobile node i accepts content from source i , i.e., ⎞ ⎛ B Q−1   (11.12) φi∗ (θ, ω = 3)⎠ , τi'i (S) = νi,li αi μˆ i ⎝ b=Jˆ i q=0

for i, i ∈ S, where νi,li is the probability that mobile node i will be at location li . φi∗ (θ, ω) is the solution of the linear programming model indicating the steady state probability of taking action ω at state θ for mobile node i. Let ν (i) denote a vector of νi,li . This vector can be obtained by solving the following equations: (ν (i) ) M(i) = (ν (i) ) and (ν (i) ) 1 = 1, where 1 is a vector of ones with an appropriate size. In (11.12), the term νi,li αi μˆ i accounts for the content arrival rate at mobile node i. The  Q−1 ∗ term Bb=Jˆ q=0 φi (θ, ω = 3) is for the case in which the mobile node has enough i energy, the content queue is not full, and the action taken is to accept content from content source i . Given a coalition S of which the mobile node is a member, the total content delivery rate perceived by mobile node i is obtained from  τim = τi'i (S). (11.13) i ∈S

Furthermore, the total content delivery rate of a “content source i” is obtained from  τi 'i (S). (11.14) τis = i ∈S

τis can be considered as the total gain/benefit obtained by mobile node i when it cooperates and forms a coalition with other nodes. Thus, for coalition formation, this total content delivery rate will define the payoff of the mobile node. We apply Little’s law to obtain the content delivery delay. The average number of items of content in the content queue of the mobile node i is obtained from q=

Q B   

qφi∗ (θ, ω).

ω∈ l∈L b=0 q=0

10 Mar 2017 at 08:08:03, .012

(11.15)

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Then, the average delivery delay is obtained from d=

11.3.3

q . τim

(11.16)

Coalition Formation Among Mobile Nodes We consider coalition formation among mobile nodes to achieve the highest possible long-term utility. While typical coalition formation games consider only a single-stage payoff, we adopt a framework of repeated coalition formation that is able to analyze the cooperation, deviation, and punishment behaviors. •

•

•

Cooperation. Because mobile nodes visit content sources opportunistically, if they have enough resources in terms of energy and storage space, they can cooperate to help each other to deliver content from their content sources to gateways. Deviation. Within a framework of cooperation, a mobile node can deviate by ceasing to help other mobile nodes. Those nodes will keep helping the deviator. This reduces their content delivery rates while that of the deviator is still high. Thus, the mobile node has a motivation to deviate from cooperation. Punishment. After a mobile node has deviated, some of the rest of the mobile nodes will observe the drop in their content delivery rate, and be able to detect the deviator. These mobile nodes can punish the deviator by ceasing to help the deviator. This will reduce the content delivery rate of the deviator.

With deviation and punishment, the mobile node has to weight whether the deviation will yield them sufficient gain or not. This has to be weighted over a long-term period. If the potential of cooperation is larger than the benefit of deviation, none of the mobile nodes will deviate. We describe repeated coalition formation in the following. Repeated coalition formation is based on classical coalition formation [30]. In this game, the mobile nodes act as players, the set of which is denoted by N . We consider a non-transferable utility (NTU) coalitional game among mobile nodes. The payoff is the content delivery rate, which cannot be allotted and transferred arbitrarily among the mobile nodes. Here N , which is the set of all players, is the grand coalition. The payoff of player i is defined as the total discounted content delivery rate from source i over time, i.e., xi (S) = (1 − δ)

∞ 

δ t τis (S, t),

(11.17)

t=0

for i ∈ S, where δ (0 < δ < 1) is the discount factor and τis (S, t) is the total content delivery rate from source i at time period t. This rate is obtained from (11.14). Here, τis (S, t) is the instantaneous payoff, which is the payoff the mobile node receives if it decides to form or not to form a coalition. xi (S) is the long-term payoff.

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The mobile nodes aim to form coalitions that maximize their long-term payoff xi (S), ∀i ∈ N . If there is a deviator, punishment will be invoked. That is, the mobile nodes in the coalition will not allow the deviator to join the coalition again. We consider two punishment schemes. •

•

Trigger. Under this scheme, the mobile nodes will prevent the entrance of the deviator into the coalition forever. However, the trigger scheme is a harsh punishment that may be neither efficient nor necessary. As the mobile nodes punish the deviator, their long-term payoff will be adversely affected Punish-and-forgive. Under this scheme, the mobile nodes will punish the deviator for T − 1 time periods, where T is referred to as the punishment duration. If T is large, the punishment is severe, and the player will be less likely to deviate. However, this will be at the cost of a lower long-term payoff for other mobile nodes. Then, after the punishment period is over, the deviator will be allowed to join the coalition again.

In terms of the cooperation, deviation, and punishment, a coalition S is stable if it is internally and externally stable. •

•

Internal stability. A coalition S is internally stable if no mobile node can obtain a higher long-term payoff by deviating from coalition S. The condition for internal stability is that xi (S) > xi ({i}), for all i ∈ S. That is, the long-term payoff xi (S) of all the mobile nodes in a coalition S must be strictly larger than that achieved if any mobile node deviates and acts alone xi ({i}). External stability. A coalition S is externally stable if it cannot merge with another coalition S  while yielding higher long-term payoffs for all players in the new coalition S ∪ S  . For mobile node i in coalition S, the long-term payoff is given by 9∞  :   t xi (S) = (1 − δ) δ τi 'i (S) , =



t=0

i ∈S

τi 'i (S).

(11.18)

i ∈S

 Here, i ∈S τi 'i (S) is the total content delivery rate of content source i, which is the instantaneous payoff of player i. If player i deviates from coalition S during time period T0 , the long-term payoff will be given by ⎞ ⎛ 9T −1   0    xiD (S) = (1 − δ) δt τi 'i (S) + δ T0 ⎝τi'i ({i}) + τi 'i (S)⎠ , t=0

+

T 0 +T t=T0 +1

i ∈S

δ t τi'i ({i}) +

∞ 

 δt

t=T0 +T+1

10 Mar 2017 at 08:08:03, .012

i ∈S \{i}



i ∈S

:

τi 'i (S)

,

(11.19)

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where • •

•

 the first and last terms i ∈S τi 'i (S) account for the total content delivery rates achieved if player i were still in the coalition;  the second term τi'i ({i}) + i ∈S \{i} τi 'i (S) is the content delivery rate of the deviator i plus the total content delivery rate from the innocent players in the coalition; and the third term τi'i ({i}) accounts for the content delivery rate when the mobile nodes other than i punish the deviator i.

xiD (S) can be expressed as follows: ⎛

⎞

⎟ ⎜ ⎟ ⎜  ⎟ ⎜ ⎟  − τ ({i}) + τ (S) ({i}) xiD (S) = (1 − δ)δ T0 ⎜ τ i'i i 'i ⎟ ⎜ i'i !" # ⎟ ⎜  i ∈S \{i} ⎝ !" # Payoff under punishment⎠ Payoff from deviation      1 − δ T0 + δ T0 +T τi 'i (S) + i ∈S

!" # Payoff from cooperation

 T  δ 0 − δ T0 +T , τi'i ({i}) !" # Payoff under punishment log (K1 /K2 ) , T > max i log δ     − τi'i ({i}) + τi 'i (S) τi 'i (S) K1 = +

i ∈S

!" # Payoff from cooperation ⎛

(11.20)

(11.21)

i ∈S \{i}

!" # Payoff from deviation

⎞

⎜ ⎟ ⎜ ⎟  ⎜ ⎟ ⎜ ⎟, + δ ⎜τi'i ({i}) + τi'i ({i}) τi 'i (S) − ⎟ !" # ⎜ ⎟ i ∈S \{i} ⎝ ⎠ Payoff under punishment !" #  K2 =

Payoff from deviation   − τi 'i (S)

i ∈S

!" # Payoff from cooperation

. τi'i ({i}) !" # Payoff under punishment

(11.22)

(11.23)

For internal stability, the long-term payoff achieved by every mobile node in the same coalition S must be larger than that achieved by deviating, i.e., xi (S) > xiD (S) for all i ∈ S. In this case, the condition in (11.21) must be met. Additionally, we can obtain the minimum value of the punishment duration T to achieve internal stability. 10 Mar 2017 at 08:08:03, .012

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For the trigger punishment scheme, the condition for internal stability of the coalition S is that xi (S) > xi ({i}), for all i ∈ S. If the deviator i deviates from the coalition S during time period T0 , the long-term payoff will become xiD (S) = (1 − δ)

= T 0 −1

 δt



⎛

τi 'i (S) + δ T0 ⎝τi'i ({i}) +

i ∈S

t=0 ∞ 

+





⎞ τi 'i (S)⎠

i ∈S \{i}

> δ t τi'i ({i}) ,

(11.24)

t=T0 +1

⎞

⎛

⎟ ⎜ ⎟ ⎜  ⎟ ⎜ D T0 ⎜ ⎟  τi'i ({i}) τi 'i (S) − xi (S) = (1 − δ)δ ⎜τi'i ({i}) + ⎟ !" # ⎟ ⎜  i ∈S \{i} ⎝ !" # Payoff under punishment⎠ Payoff from deviation ⎞ ⎛ ⎜ ⎜ ⎜ +⎜ ⎜ ⎝





i ∈S



  1 − δ T0 +

τi 'i (S)

!" # Payoff from cooperation

⎟ ⎟ δ ⎟. τi'i ({i}) !" # ⎟ Payoff under punishment ⎠ T0 ⎟

(11.25) Again, the coalition S will be internally stable if the long-term payoff of the mobile nodes in the coalition is larger than that outside the coalition, i.e., xi (S) > xiD (S) for all i ∈ S. For the external stability, the mobile nodes must obtain higher long-term payoff by merging than by not merging, i.e., xi (S) > xi (S ∪{i}) for all i ∈ S and xi (S) > xi ({i}). We first examine the optimal policy of a mobile node in two cases. Firstly, if the mobile node is at the gateway, it can choose to transmit content or to request wireless energy transfer. Secondly, if the mobile node is at the content source, the node can choose whether to accept content or not. We set the content blocking probability for a node’s own content source to 0.1, while we set no requirement for the other content sources. Figure 11.6 shows the optimal policy in terms of the probability of taking a certain action given the queue state and energy state (i.e., the number of items of content waiting in the content queue and the energy level of the energy storage, respectively). In particular, Figures 11.6(a) and (b) correspond to the case in which the mobile node is at the gateway, while Figures 11.6(c) and (d) correspond to the cases in which the node is at its own content source and at other content sources. From Figures 11.6(a) and (b), we observe that, when the mobile node is at the gateway, the node will place a request for wireless energy transfer if the energy level is low and/or the queue state is small. This is to ensure that it has sufficient energy to receive content from content sources and to transmit content to the gateway. In contrast, if the energy level is high and/or the queue is large, a mobile node will be more likely to transmit content to the gateway to clear its 10 Mar 2017 at 08:08:03, .012

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(a)

(b) 100

100

90

90

80

80

70 Probability of requesting for energy 1 0.5 0

70

60

60

50 40

Probability of packet transmission 1 0.5 0 0 5 0 Queue state

Energy state

30 20 10

0 5 0 Queue state

50 40

Energy state

30 20 10

(d)

(c)

100

100 90

90 80

80 70

70 Probability of receiving packet (own source)

60 50 40 30

1 0.5 0

20 10 0 5 0 Queue state

Energy state

60

Probability of receiving packet (other sources) 1 0.5 0

50 40 30

Energy state

20 10 0 5 0 Queue state

Figure 11.6 Optimal policy of a mobile node to (a) request energy transfer, (b) transmit a packet, (c) receive a packet from its own content source, and (d) receive a packet from other content sources.

content queue. Figure 11.6(c) shows that a mobile node will mostly accept content from its own content source, while Figure 11.6(d) indicates that a mobile node can limit its acceptance of content from other content sources. The probability that a given mobile node accepts content from other content sources depends on whether the mobile node cooperates with the mobile node corresponding to that content source or not. Moreover, we observe that the optimal policy of a mobile node does not have a threshold policy for the CMDP. Then, we compare the content delivery rate of mobile nodes 1 and 2 with and without cooperation (Figure 11.7). The content generation/packet generation rate of source 2 is varied. •

•

Without cooperation, the delivery rate of source 1 is not affected by the content generation rate of content source 2. However, the delivery rate of content source 2 increases as its generation rate increases. With cooperation, the delivery rates of both content sources are higher than that achieved without cooperation. However, while the delivery rate of content source 2 increases constantly, that of content source 1 will decrease. Because mobile node 1 must use its resources to deliver content from source 2, it has less resources for source 1. There is a point at which the delivery rate of content source 1 with cooperation with content source 2 becomes lower than that obtained in the case without cooperation. In this case, mobile node 1 will choose not to cooperate with node 2. 10 Mar 2017 at 08:08:03, .012

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0.02 0.018 0.016

Source 1 (without cooperation) Source 2 (without cooperation) Source 1 (with cooperation) Source 2 (with cooperation)

Delivery rate

0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 0.01

0.02

0.03 0.04 0.05 0.06 Content generation rate of source 2

0.07

0.08

Figure 11.7 Packet delivery rates of content sources 1 and 2 versus packet generation rate of content source 2.

0.16

Content generation rate of source 1

0.14

E {1},{2},{3}

0.12

C {1},{2,3}

0.1

B {1,2},{3}

0.08 F {1},{2},{3}

0.06

0.04 A {1,2,3}

0.02

0

D {1,3},{2}

0

0.02

0.04

0.06 0.08 0.1 0.12 Content generation rate of source 2

0.14

Figure 11.8 Stable coalitions for different content generation rates of content sources 1, 2,

and 3.

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0.16

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We apply repeated coalition formation and analyze the stable coalition among three mobile nodes. The content generation rates of sources 1 and 2 are varied, while that of source 3 is fixed at 0.01. We can expect different ranges of content generation rates of sources 1 and 2 that lead to stable coalitions (Figure 11.8). These ranges are named A, B, C, D, E, and F, and we make the following observations. •

•

•

•

•

•

Region A. The content generation rates of all the content sources are relatively small. Therefore, all of them will tend to cooperate because none of them can exploit the resources of other mobile nodes. Therefore, the grand coalition {1, 2, 3} is stable. Region B. The content generation rates of content sources 1 and 2 are much larger than those of content source 3. Therefore, content source 3 will not cooperate and form a coalition with content sources 1 and 2. By contrast, content sources 1 and 2 can help each other since their content generation rates are not much different. Therefore, the coalitions {1, 2}, {3} are stable. Region C. Content source 1 generates much more content than do sources 2 and 3. Therefore, mobile nodes 2 and 3 will form a coalition, but not with mobile node 1. The coalitions {1}, {2, 3} are stable. Region D. Differently from region C, in region D, content source 2 generates much more content than sources 1 and 3. Therefore, the coalitions {1, 3}, {2} are stable. Region E. Content source 1 generates much more content than content source 2, which in turn generates much more content than content source 3. Therefore, none of them will form a coalition. Only singletons {1}, {2}, {3} are stable. Region F. Content source 2 generates much more content than content source 1, which in turn generates much more content than content source 3. Therefore, none of them will cooperate and the coalitions {1}, {2}, {3} are stable.

For wireless-powered DTNs and our performance analysis and optimization framework, we make the following observations. •

•

•

•

At different locations, a mobile node can take different actions to transfer energy and content. Its optimal policy, which is a mapping from the state to the action, can be optimized using a CMDP to maximize the content delivery rate while meeting the content blocking requirements. Mobile nodes have motivation to improve their content delivery rates by cooperating with other mobile nodes. However, not all mobile nodes want to cooperate, depending on the parameters and setting. In a coalition, a mobile node can deviate and exploit the resources of innocent nodes to gain a higher content delivery rate. However, the innocent nodes will be affected and they can invoke punishment of the deviator. Although the punishment is intended to prevent deviation, it adversely affects the performance of all mobile nodes. Stable coalitions can be obtained considering the long-term payoffs of the mobile nodes, taking cooperation, deviation, and punishment into account. 10 Mar 2017 at 08:08:03, .012

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403

Delay-Limited Communication in MANETs Delay is an important aspect of performance to many real-time applications. The authors of [31] study delay-limited communication in wireless-powered mobile ad-hoc networks. A mobile node moves and is able to receive wireless energy, e.g., from a wireless charger. The mobile node uses the energy to transmit delay-sensitive data. In particular, the data must be successfully transmitted before a certain deadline. Otherwise, such data will be discarded and considered lost. Therefore, the mobile node can optimize its data transmission policy to minimize the data loss due to violating the delay deadline. This is equivalent to maximizing the throughput, which is the amount of data successfully transmitted before the deadline per unit time. Given a set of mobile nodes, the wireless chargers can optimize their energy transfer strategy to minimize the power cost while meeting the performance requirement of the mobile node. Finally, in the long term, wireless chargers can be deployed selectively. See Figure 11.9. The authors of [31] propose a performance analysis and optimization framework for mobile nodes and wireless chargers. The framework is composed of the following components. •

•

Mobile node optimization. With limited energy supply for a mobile node, one can optimize the transmission of delay-sensitive data. The mobile node may delay the transmission of data if its energy level is low and the deadline of the data has not been reached. Alternatively, it may have to transmit the data soon, if the deadline is approaching. The optimization of data transmission policy is performed by using a CMDP. Wireless charger optimization. When a wireless charger transfers energy to mobile nodes, it consumes power. Thus, to minimize power consumption, it has to choose when to transfer energy. Owing to the broadcast nature of the wireless energy transfer, e.g., based on RF technology, multiple mobile nodes can receive the energy. Thus, the wireless charger can employ a simple threshold scheme that

Figure 11.9 Optimal transmission policy of a mobile node, energy management strategy, and deployment of wireless chargers. 10 Mar 2017 at 08:08:03, .012

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•

it will release energy when the number of mobile nodes that can receive energy is larger than or equal to the threshold. The threshold has to be carefully chosen not only to minimize energy consumption, but also to supply sufficient energy to the mobile nodes. Wireless charger deployment. It is important to optimize the deployment of wireless chargers. Given a set of candidate locations, the chargers should be deployed to maximize the opportunity to supply energy to the mobile nodes. However, the cost of deployment has to be taken into account.

These three components are interrelated. The optimal transmission policy of a mobile node involves observing the energy supply, which is an outcome of the energy management of a wireless charger. The wireless charger observes the data loss performance of the mobile nodes together with the available wireless charger to optimize the energy management. The power consumption of wireless chargers affects the optimal wireless charger deployment. In the literature, wireless energy optimization is performed for mobile nodes. For example, the authors of [32] introduce an RFID scheduling algorithm. The algorithm considers the tradeoff between the amount of energy harvested and the throughput. An MDP is adopted to obtain an optimal policy that maximizes the read probability of an RFID tag. The authors of [33] formulate a partially observable MDP (POMDP) to derive an optimal policy for mode selection of a sensor node to receive energy or transmit data under the condition that the channel state is not perfectly known by the sensor node. The authors of [34] study wireless energy harvesting in cooperative networks. In the network, a relay node can receive energy from source nodes and use that energy to forward data from the source nodes. The performance analysis of the cooperative network when the greedy policy uses available energy for packet forwarding is analyzed using a Markov chain. The analysis is able to obtain the outage probability of the relay transmission. However, the delay performance is also important and has been analyzed in the literature e.g., [35, 36]. For example, the authors of [35] impose an average delay constraint on data transmission with wireless energy harvesting. The authors of [36] introduce an MDP to obtain an optimal data transmission policy for delay-limited data. Apart from wireless energy optimization, energy management and energy source deployment are also important issues, especially in the green communication context. For example, there is a tradeoff between the number of relay stations and the number of base stations. With more relay stations, the user performance improves, but at the cost of more energy consumption. The analysis has been done in [38]. The authors of [39] analyze the energy consumption of different base station deployment strategies. They also derive an optimal cell size to achieve minimum energy consumption. The authors of [40] propose deploying a dense array of micro base stations to reduce the energy consumption of the entire network. The analysis shows that a substantial improvement in performance and decrease in the amount of energy needed to supply the infrastructure can be achieved.

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11.4.1

405

System Model A mobile node can transmit data and harvest wireless energy. The data transmission is from the mobile node to any base station. The data are delay-sensitive, and must be transmitted before a certain deadline. If the data cannot be transmitted before the deadline, they will be discarded and considered lost. After the data have been successfully transmitted or discarded, new data will be generated, awaiting transmission. The error control employed is that the data will be re-transmitted until they have been successfully received by the base station. The mobile node has an energy storage device, i.e., a battery, with a maximum capacity of E units of energy. Transmitting data consumes one unit of energy from the energy storage device. If the energy storage device is empty, the mobile node cannot transmit data. The mobile node receives energy when it visits the coverage area of the wireless charger and the charger releases energy. When the charger transfers energy, it is said to be active. We assume broadcast energy transfer such that multiple mobile nodes within the coverage area can harvest energy simultaneously from the charger [41, 42]. The mobile node receives one unit of energy with probability cl from a charger located at location l. This probability depends on the energy management of the wireless charger, i.e., the decision regarding whether to transfer energy or not. A mobile node moves in a service area. The service area is discretized into a set of locations denoted by L = {0, 1, . . . , L}. Location l = 0 denotes the case in which the mobile node is not within the coverage area of any wireless charger. Locations l ∈ {1, . . . , L} denote cases in which the mobile node is within the coverage area of one of the chargers. It is assumed that there is no overlap between the coverage areas of any two charger. Figure 11.10 shows an example of a service area with four locations with wireless chargers. The change of location of the mobile node from location l to location

Figure 11.10 Service area of delay-limited data transmission with wireless energy harvesting.

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l is denoted by the probability Ml,l . The corresponding transition probability matrix is defined as follows: ⎡

M0,0 ⎢ .. M=⎣ . ML,0

· · · M0,l .. .. . . · · · ML,l

··· .. . ···

⎤ M0,L .. ⎥ . . ⎦

(11.26)

ML,L

Successful transmission of data by the mobile node at location l is denoted by κl . The mobile node employs different interfaces for data transmission and wireless energy harvesting. Thus, they can be performed simultaneously irrespective of the location.

11.4.2

Data Transmission Policy of a Mobile Node A CMDP is formulated to obtain an optimal data transmission policy. The state space of a mobile node is given by   = (D, E , L ); D ∈ {0, 1, . . . , D}, E ∈ {0, 1, . . . , E}, L ∈ L ,

(11.27)

where • • •

D represents the delay state of the current data/packet, E represents the energy level of the battery, and L represents the location of the mobile node.

D is the delay deadline and E is the energy storage capacity. Let θ = (d, e, l) ∈ be a composite variable, where d, e, and l have the same meanings as those of D, E , and L , respectively. The action space is defined as  = {0, 1}, where 1 and 0 represent the actions “transmit” and “do not transmit” (i.e., “wait”), respectively. We formulate the CMDP to obtain an optimal data transmission policy of the mobile node. The objective is to minimize the data loss probability. Data are lost if they cannot be transmitted before the deadline. Additionally, the policy has to ensure that the throughput of the mobile node is maintained above or at the threshold denoted by T. Let JL and JT denote the steady state loss probability and throughput. They are defined as follows: 1 E ((θt , δt )) , t 

(11.28)

1 t

(11.29)

t

JL = lim sup t→∞

JT = lim sup t→∞

t =1 t 

E (ϒ(θt , δt )) ,

t =1

where θt ∈ is the state variable and δt ∈  is the action variable of the mobile node at time t . (·) is the immediate data loss probability function and ϒ(·) is the throughput function. Next, we derive these functions. 10 Mar 2017 at 08:08:03, .012

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The immediate data loss probability is obtained from ⎧ 1, d = D and e = 0, ⎪ ⎪ ⎨ 1, d = D and δ = 0, (θ , δ) = ⎪ 1 − κl , d = D and δ = 1, ⎪ ⎩ 0, otherwise.

407

(11.30)

Data loss happens if the deadline is reached and • • •

the battery is empty, the mobile node decides not to transmit the data, and the transmission of data is unsuccessful, with probability 1 − κl . The immediate throughput is obtained from  κl , e > 0 and δ = 1, ϒ(θ, δ) = 0, otherwise.

(11.31)

The data are successfully transmitted if the deadline is not reached, the battery is not empty, and the mobile node decides to transmit the data. The CMDP aims to obtain an optimal data transmission policy. A randomized policy π is a mapping from the state to the action. The optimization formulation is expressed as follows: min JL (π ) π

subject to JT (π ) ≥ T.

(11.32)

Here, the optimal policy is denoted by π ∗ (θ, δ) for θ ∈ and δ ∈ . It is the probability of taking the action δ when the current state of the mobile node is θ. To obtain the optimal policy, the optimization is transformed into an equivalent linear programming model [29]. Let φ(θ , δ) denote the steady state probability of state θ and action δ. The equivalent linear programming model is expressed as follows:  φ(θ , δ)(θ , δ) min φ(θ ,δ)

subject to

θ∈ δ∈



φ(θ , δ)ϒ(θ, δ) ≥ T,

θ∈ δ∈



φ(θ  , δ) =

δ∈





φ(θ , δ)P(θ  |θ , δ),

θ  ∈ ,

θ∈ δ∈

φ(θ , δ) = 1,

φ(θ , δ) ≥ 0,

(11.33)

θ∈ δ∈

where P(θ  |θ , δ) denotes the probability that the action δ is taken and the state changes from θ to θ  . • • •

The objective in (11.55) (given in Section 11.5.2) is to minimize the loss probability. The first constraint in (11.33) is to maintain the throughput at the threshold. The third constraint in (11.55) satisfies the Chapman–Kolmogorov equation. 10 Mar 2017 at 08:08:03, .012

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In terms of the optimal solution of the linear programming model, denoted by the optimal transmission policy of the mobile node is obtained from

φ ∗ (θ, δ),

 φ ∗ (θ, δ) φ ∗ (θ, δ  ) > 0. , for θ ∈ and ∗  δ  ∈ φ (θ, δ ) 

π ∗ (θ, δ) =  

(11.34)

δ ∈

∗ (θ, δ  )

= 0, then the specific action “wait” is taken. The important performance metrics of the mobile node can be obtained under the optimal policy π((d, e, l), δ). First, we obtain the steady state probability of the mobile node by solving the following equations η Pπ = η and η 1 = 1, where 1 is a vector (with an appropriate size) of ones, Pπ is the transition probability matrix when the policy π is applied, and η is the vector of steady state probabilities, the element of which is η(d, e, l). The delay distribution, which indicates the probabilities of time used to transmit data successfully, is obtained from

If

δ  ∈ φ

β(d) =

L E  

η(d, e, l)π((d, e, l), 1)κl .

(11.35)

e=1 l=0

The data are successfully transmitted if the mobile node takes the action “transmit” (i.e., δ = 1) and the battery has enough energy. The average delay can be obtained from d=

D 

dβ(d).

(11.36)

d=0

The throughput of the mobile node is obtained as follows: υ=

L  E  D 

η(d, e, l)π((d, e, l), 1)κl .

(11.37)

e=1 l=0 d=0

It is the amount of data successfully transmitted per time unit before the deadline. The data loss probability is obtained from λ=

L  1 

η(D, 0, l)π((D, 0, l), δ)

l=0 δ=0

+

!" (1)

#

  η(D, e, l) π((D, e, l), 1)(1 − κl ) + π((D, e, l), 0) , !" # !" # l=0 (2) (3)

L E   e=1

(11.38)

where • • •

(1) accounts for the data loss when there is no sufficient energy in the storage, (2) accounts for the data loss because of unsuccessful transmission, and (3) accounts for the data loss because of not transmitting data.

All the losses happen when the delay deadline D is reached. 10 Mar 2017 at 08:08:03, .012

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11.4.3

409

Energy Management of Wireless Charger To efficiently transfer energy to mobile nodes, the wireless charger may want to transfer energy only when there are enough mobile nodes in its coverage area. This determines the probability cl of the mobile node. There are three simple distributed energy management strategies for the wireless charger. •

Always active. The wireless charger always transfer wireless energy whenever there is at least one mobile node in its coverage area. In this case, the probability of receiving energy is cl = 1. Probabilistic. The wireless charger at location l transfers energy with a probability σl . The mobile node can receive this energy with probability cl = σl . Threshold-based. In this case, the wireless charger can detect the mobile nodes which are within its coverage area. The wireless charger at location l transfers energy if the number of mobile nodes in the coverage area is equal to or larger than the threshold ωl .

• •

For threshold-based energy management, the probability that the mobile node receives the energy is derived as follows. First, we obtain the steady state probability that the mobile node will be at a certain location. Its corresponding vector is denoted by μ and the element of this matrix is μl . The vector can be obtained by solving μ M = μ and μ 1 = 1, where M is the mobility transition matrix as defined in (11.26). For N mobile nodes, the probability that there are nl mobile nodes at location l is obtained from

φ(n0 , . . . , nL , N, μ0 , . . . , μL ) =

⎧ ⎪ ⎨ ⎪ ⎩

N! (μ0 )n0 · · · (μL )nL , n0 ! . . . nL !

L 

nl = N,

l=0

0,

otherwise, (11.39) which is basically a multinomial distribution. Then, we derive the probability that a particular mobile node and at least ωl − 1 other nodes are at location l as follows: γˆl (ωl ) = ⎛ ⎜ ⎜ ⎜ ⎜  n =ωl −1 ⎝ N−1 

l

⎞  (n0 , . . . , nl−1 , nl+1 , . . . , nL ) n0 + · · · + nl + · · · + nL = N − 1

⎟ ⎟ μl φ(n0 , . . . , nl , . . . , nL , N − 1, μ0 , . . . , μL )⎟ ⎟, ⎠ (11.40)

where nl ≥ 0 for l = l . Then, the mobile node receives energy with the probability cl =

γˆl (ωl ) . μl

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(11.41)

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The probability that the wireless charger at location l transfer energy is obtained from ⎛ ⎞ N ⎜   ⎜ ⎜ Al = ⎜ nl =ωl ⎝ (n0 , . . . , nl−1 , nl+1 , . . . , nL )

⎟ ⎟

φ(n0 , . . . , nl , . . . , nL , N, μ0 , . . . , μL )⎟ ⎟. ⎠

n0 + · · · + nl + · · · + nL = N

(11.42) If the wireless charger at location l consumes wl unit of power when it transfers energy, then the average power consumption is W l = wl Al .

(11.43)

Now, we aim to optimize the threshold of the wireless chargers. Clearly, the probability that the mobile node receives energy is a non-increasing function of a threshold ωl . Given the transmission policy π(θ, δ), we can determine the feasible region, i.e., a set of thresholds, of all wireless chargers within which the data loss probability of the mobile nodes can be maintained below the loss requirement R as follows:   (11.44) (R) = ω = (ω1 , . . . , ωL ); λ(ω1 , . . . , ωL ) ≤ R , where λ(·) is the data loss probability obtained from (11.43). The data loss probability has to be defined as a function of the thresholds of all of the wireless chargers. To minimize the total power consumption of all of the wireless chargers, the optimization can be formulated for the feasible region (R) as follows: min ω

L 

Wl (ω),

Wl (ω) = wl Al (ω),

l=1

subject to ω ∈ (R)

(11.45)

where Al (ω) is the probability that wireless charger at location l transfers energy, and Wl (ω) is the power consumption of the wireless charger. They are defined as functions of a set of thresholds ω. The optimal solution ω∗ can be obtained by enumeration.

11.4.4

Wireless Charger Deployment While the optimal data transmission policy of a mobile node and energy management of a wireless charger are performed in a short-term fashion, we can optimize the deployment of the wireless chargers at a set of candidate locations in such a way as to minimize the cost in the long term. Let Lˆ denote a set of candidate locations and let Wl (ω, LD ) denote the power consumption of a wireless charger at location l if this wireless charger is in operation. The power consumption is defined as a function of LD , i.e., a set of ˆ The optimization for the wireless charger deployed wireless chargers, where LD ⊆ L. deployment is defined as follows:

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min LD

411



 Wl† (ω, LD ) + Xl ,

l∈LD

ˆ subject to LD ⊆ L,

(11.46)

where Xl is the deployment cost of a wireless charger at location l ∈ LD . Here Wl† (ω, LD ) is the minimum power consumption of the wireless charger at location l. This minimum power consumption still ensures that the data loss requirement of mobile nodes is met. The optimal solution of the wireless charger deployment optimization can be obtained by enumeration. Finally, the optimal data transmission policy of the mobile node and the energy management and deployment of the wireless chargers are integrated. Algorithm 11.1 is used to obtain their solution. The algorithm first determines a set of candidate locations. Given a certain location, the optimal threshold for the energy management of the wireless charger is obtained. Algorithm 11.1 Algorithm to obtain an optimal data transmission policy of a mobile node, integrated with energy management and deployment of wireless chargers repeat Select a set of candidate locations for wireless chargers to be deployed LD . Obtain optimal thresholds of energy management for a wireless charger at location l ∈ LD . Obtain an optimal transmission policy of the mobile node given the wireless chargers at the candidate locations and the thresholds of the energy management strategy. until The set of deployed wireless chargers achieving the lowest total cost has been found.

Figure 11.11(a) shows the optimal data transmission policy when the mobile node is at locations # = 0 without any charger, and Figure 11.11(b) shows the policy when the mobile node is within range of a wireless charger. We observe that, when the delay state is large and close to the deadline at T = 10 and the energy level is high, the mobile node inclines toward transmitting the data. Otherwise, the mobile node will wait until it has replenished the energy in its battery. This result arises from the fact that the mobile node has to conserve energy for future transmission, especially in locations without any wireless charger. Figure 11.12 shows the total power consumption of wireless chargers when the number of mobile nodes in the service area is varied. As the number of mobile nodes in the service area increases, the wireless chargers will transfer energy more frequently. Consequently, the total power consumption increases. However, since there is more energy supply, the performances of the mobile nodes improve including lower average delay, lower loss probability, and higher throughput.

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0.6 0.4 0.2 0 10

9

8

7

6

5

4

3

2

1

0

0

1

2

3

4

5

6

7

8

9

10

1 0.8 0.6 0.4 0.2 0 10

9

8

7

6

5

4

3

2

Delay

1

0

0

1

2

3

4

5

6

7

8

9

10

Delay

Energy state

Energy state

Figure 11.11 Optimal data transmission policy when a mobile node is (a) not at a wireless charger

and (b) at a wireless charger. 3.5 Threshold for wireless charger to transfer energy=2 Threshold for wireless charger to transfer energy=3 Threshold for wireless charger to transfer energy=4

3 Total power consumption

Probability of taking action “transmit’’

1 0.8

Probability of taking action “transmit’’

(b)

(a)

2.5 2 1.5 1 0.5 0

0

2

4

6

8

10

12

14

16

18

20

Number of nodes in service area Figure 11.12 Total power consumption of all wireless chargers when the number of mobile nodes

in a service area is varied.

Figure 11.13 shows the total cost, which is composed of the deployment cost and the total power consumption cost, when the number of wireless chargers to be deployed is varied. With different loss requirements R, there is an optimal number of wireless chargers to be deployed such that the total cost is minimized. We observe that, with tight loss requirements (i.e., R = 0.01 and R = 0.05), having one wireless charger is not sufficient to meet the loss requirement, and thus the results for these cases are excluded from the figure. 10 Mar 2017 at 08:08:03, .012

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1.3

413

Loss requirement = 0.01 Loss requirement = 0.05 Loss requirement = 0.10 Lowest total cost

1.2 1.1

Total cost

1 0.9 0.8 0.7 0.6 0.5 0.4

1

2 3 Number of wireless chargers

4

Figure 11.13 Total cost versus the number of wireless chargers.

11.5

Mobile Energy Sharing In addition to optimizing the data transmission policy as mentioned above, mobile nodes can share the energy available in their energy storage devices so that they can use it for transmitting data. This problem of energy sharing in mobile networks is considered in [43]. In particular, the concept of the mobile energy sharing network that allows mobile nodes to transfer energy among each other directly when they move and meet each other is introduced. This energy sharing is in addition to the energy supply from wireless chargers, and can reduce the chance of energy depletion when the mobile nodes need it to transmit data or to run mobile applications. The performance optimization of the energy sharing policy is based on a constrained Markov decision process (CMDP). The CMDP is for two mobile nodes that agree to share energy with each other. The objective of the CMDP is to minimize the energy outage probability, which is the probability that the battery of a mobile node is depleted. In terms of fairness, the energy transfer policy has to ensure that neither one of a pair of mobile nodes will experience an energy outage probability higher than that without energy sharing. Then, to determine the mobile nodes which are best matched to share their energy, a matching algorithm based on linear programming is proposed. Figure 11.14 shows these major optimizations for the mobile node matching and energy sharing policy. While the matching algorithm yields the matching structure, which is a set of pair of matched mobile nodes, the energy sharing policy provides the energy outage probabilities of mobile nodes so that they can adapt their matching. Some works consider energy transfer in a mobile environment. The authors of [44] explore the concept of distributable energy in mobile robot networks. In such networks, multiple robots performing certain tasks regularly need energy supply. Energy 10 Mar 2017 at 08:08:03, .012

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Figure 11.14 Matching algorithm and energy sharing policy.

replenishment interrupts the action of the robots, preventing them from continuously completing the tasks. Therefore, it is beneficial for the robots to be able to share energy, for example, by exchanging batteries, with other robots. To efficiently share energy, the authors introduce coordination control and optimization for a path planning and battery exchange policy whereby the mobile robots can meet and swap their batteries. In a similar network, the authors of [45] present an algorithm that allows docking stations acting as chargers to be deployed at certain locations to replenish energy for mobile robots. The algorithm is based on optimization of docking station deployment with the objective of minimizing the cost of replenishing energy for all robots in the network. The authors of [46] introduce a framework to support mobile-to-mobile energy replenishment for robotic sensor networks. Here, mobile chargers are deployed to transfer energy to the robots. The authors also develop an algorithm to schedule energy charging that incorporates charging delay and travel time. The objective is to minimize the travel distance of the mobile charger.

11.5.1

System Model Figure 11.15 shows the system model of the mobile energy sharing network. In the network, multiple mobile nodes have an energy storage device, i.e., a battery, to store energy received from chargers. The mobile nodes consume energy from their batteries to transmit data or to run mobile applications. Two mobile nodes can be matched to share their energy. In particular, when they meet, their energy can be transferred, for example, from the node with a higher energy level to the node with a lower energy level. The transfer of a unit of energy from one node to another node is successful with probability α in a time slot.

11.5.2

Optimal Energy Sharing We first consider an optimal energy sharing policy, which is the lower component in Figure 11.14. To obtain the optimal policy, the CMDP is formulated for two matched mobile nodes. Let M = {i, j} denote the set of matched mobile nodes i and j. They can 10 Mar 2017 at 08:08:03, .012

Mobile Ad-Hoc Networks and Delay-Tolerant Networks

415

Figure 11.15 System model for a mobile energy sharing network.

transfer energy between one another depending on their states, the space of which is defined as follows:    = Bi , Bj , Di , Dj , M ; Bi ∈ {0, 1, . . . , Bi },  (11.47) Bj ∈ {0, 1, . . . , Bj }, Di , Dj ∈ {0, 1}, M ∈ {1, . . . , 5} . The states are described as follows. •

•

•

Bi and Bj represent the energy levels in the batteries of matched mobile nodes i and j, respectively. Bi and Bj are the maximum capacities of the batteries of nodes i and j, respectively. Di and Dj represent the energy consumption states of nodes i and j, respectively. Di and Dj take values 0 or 1. Di , Dj = 1 if the mobile nodes consume one unit of energy in a time slot. Otherwise, Di , Dj = 0 if the mobile nodes do not consume energy. M represents the contact state of mobile nodes. There are five possible states denoted by the following numerical values. – – – – –

M = 1. The two nodes do not meet each other and do not visit the charger. M = 2. The two nodes do not meet each other and node i visits the charger. M = 3. The two nodes do not meet each other and node j visits the charger. M = 4. Both nodes visit the charger. M = 5. The two nodes meet and do not visit the charger.

Let ω = (bi , bj , di , dj , m) denote a composite state variable corresponding to the states Bi , Bj , Di , Dj , and M, respectively. Here, energy transfer between two nodes can be performed when m = 5. In this case, for m = 4, where both nodes visit chargers, it is natural to assume that they do not need to transfer energy between one another. The transition probability matrix of the contact state is denoted by M, the element of which is Mm,m representing the probability that the contact state is m in the current time slot and becomes m in the next time slot. Then, Di and Dj denote the transition (j) (i) matrices for the states di and dj , respectively. Their elements Dd,d and Dd,d denote the probability that the energy consumption state changes from d to d for mobile nodes i and j, respectively. 10 Mar 2017 at 08:08:03, .012

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Thus, the action space for both mobile nodes is defined as follows:  A(m) =

{0, 1, 2}, {0},

m = 5, otherwise.

(11.48)

Here, the action space depends on the contact state m, the value of which is defined as follows: • • •

0 represents the action that both nodes remain idle, 1 represents the action that node i transfers one unit of energy to node j, and 2 represents the action that node j transfers one unit of energy to node i. To derive the transition probability matrix, different cases have to be considered.

• •

•

•

•

di = 0, dj = 0, m = 1. Neither of the mobile nodes consumes energy, and they do not meet each other. Thus, there is no change to the energy levels of both nodes. di = 0, dj = 0, m = 2. Neither of the mobile nodes consumes energy, and only mobile node i visits the charger. Thus, the energy level of mobile node i can increase, while that of mobile node j remains the same. di = 0, dj = 0, m = 3. Neither of the mobile nodes consumes energy, and only mobile node j visits the charger. Thus, the energy level of mobile node j can increase, while that of mobile node i remains the same. di = 0, dj = 0, m = 4. Neither of the mobile nodes consumes energy, and both mobile nodes visit the charger. Thus, the energy levels of both mobile nodes increase. di = 0, dj = 0, m = 5. Neither of the mobile nodes consumes energy, and neither of the mobile nodes visits the charger, but they meet each other. The energy level of each mobile node depends on the action a. – –

– • •

•

•

a = 0. No energy is transferred, and thus the energy levels of both mobile nodes remain the same. a = 1. Mobile node i transfers one unit of energy to mobile node j. In this case, the energy level of mobile node i decreases, while that of mobile node j increases. a = 2. Mobile node j transfers one unit of energy to mobile node i.

di = 0, dj = 1, m = 1. Only mobile node j consumes energy, and the two mobile nodes do not meet. Thus, only the energy level of mobile node j will decrease. di = 0, dj = 1, m = 2. Only mobile node j consumes energy, and only mobile node i visits the charger. Thus, the energy level of mobile node i can increase, while that of mobile node j will decrease. di = 0, dj = 1, m = 3. Only mobile node j consumes energy, and only mobile node j visits the charger. Thus, the energy levels of both mobile nodes remain the same. di = 0, dj = 1, m = 4. Only mobile node j consumes energy, and both mobile nodes visit the charger. Thus, the energy level of mobile node i increases, while that of mobile node j remains the same. 10 Mar 2017 at 08:08:03, .012

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•

di = 0, dj = 1, m = 5. Only mobile node j consumes energy, and neither of the mobile nodes visits the charger, but they meet each other. The energy level of each mobile node depends on the action a. – –

– • •

417

a = 0. No energy is transferred, and thus the energy level of mobile node i remains the same, while that of mobile node j decreases. a = 1. Mobile node i transfers one unit of energy to mobile node j. In this case, the energy level of mobile node i decreases, while that of mobile node j remains the same. a = 2. Mobile node j transfers one unit of energy to mobile node i.

(di = 1, dj = 0, m) for m = 1, . . . , 5. This is similar to the case of (di = 0, dj = 1, m). (di = 1, dj = 1, m) for m = 1, . . . , 5. This is similar to the case of (di = 0, dj = 0, m), except that mobile nodes i and j will consume one more unit of energy.

The energy sharing policy is obtained from the CMDP formulated for mobile nodes i and j as follows: min JS (π ) π

subject to JO,i (π ) ≤ Li , JO,j (π ) ≤ Lj ,

(11.49)

where • •

JS (π ) represents the steady state aggregated energy outage probability of both mobile nodes, and JO,i JO,j are the steady state individual energy outage probabilities of mobile nodes i and j, respectively.

Li and Lj are the energy outage probabilities of mobile nodes i and j when they act alone without matching. They serve as benchmarks for the mobile nodes such that, if they are matched, their performance will not be worse than that without matching. The steady state performance functions are defined as follows: 1 E (S (ωt , at )) , t 

(11.50)

1 t

E (Oi (ωt , at )) ,

(11.51)

t  1  E Oj (ωt , at ) , t 

(11.52)

t

JS (π ) = lim inf t→∞

JO,i (π ) = lim inf t→∞

JO,j (π ) = lim inf t→∞

t =1 t  t =1

t =1

where ωt ∈  is the state variable and at ∈ A is the action variable at time t. 10 Mar 2017 at 08:08:03, .012

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The immediate aggregated and individual nodes i are given by ⎧ ⎨ 1, S (bi , bj , di , dj , m) = 1, ⎩ 0,  1, Oi (bi , bj , di , dj , m) = 0,

energy outage probabilities of mobile bi = 0 and di = 1, bj = 0 and dj = 1, otherwise,

(11.53)

bi = 0 and di = 1, otherwise.

(11.54)

An energy outage occurs when a mobile node needs to consume energy, but its battery is empty. A randomized policy for energy sharing is adopted. The optimal policy is denoted by π ∗ ((bi , bj , di , dj , m)|a) = π ∗ (ω|a), which is the probability of taking action a ∈ A at state (bi , bj , di , dj , m) = ω ∈ . Again, an equivalent linear programming model is used as follows:  min φ(ω, a)S (ω, a), φ(ω,a)

subject to

ω∈ a∈A



φ(ω, a)Oi (ω, a) ≤ Li ,

ω∈ a∈A



φ(ω, a)Oj (ω, a) ≤ Lj ,

ω∈ a∈A



φ(ω , a) =

a∈A





φ(ω, a)Pω,ω (a), ω ∈ ,

ω∈ a∈A

φ(ω, a) = 1,

φ(ω, a) ≥ 0,

(11.55)

ω∈ a∈A

where Pω,ω (a) is the transition probability from the current state ω = (bi , bj , di , dj , m) to the next state ω = (bi , bj , di , dj , m ). The optimal randomized energy sharing policy can be derived from the optimal solution of the linear programming model, i.e., φ ∗ (ω, a), as follows: π ∗ (ω, a) = 

φ ∗ (ω, a) , ∗  a ∈A φ (ω, a )

(11.56)

  for ω ∈  and a ∈A φ ∗ (ω, a ) > 0. If a ∈A φ ∗ (ω, a ) = 0, then π ∗ (ω, 0) = 1 (i.e., both mobile nodes will do nothing). After obtaining the optimal solution φ ∗ (ω, a) of the linear programming model, we can obtain the steady state performance metrics. The energy outage probabilities are given by Oi =

Bj 1  5   

π ∗ ((bi = 0, bj , di = 1, dj , m)|a),

(11.57)

π ∗ ((bi , bj = 0, di , dj = 1, m)|a).

(11.58)

bj =0 dj =0 m=1 a∈A

Oj =

Bi  1  5   bi =0 di =0 m=1 a∈A

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The average amount of energy transferred from mobile node i to mobile node j is obtained from Ti→j =

Bj Bi  

π ∗ ((bi , bj , di = 0, dj = 1, m = 5)|a = 1)

bi =1 bj =0

+

j −1 Bi B 

bi =1 bj =0

+

Bj Bi  

bi =2 bj =0

+

j −1 Bi B 

bi =2 bj =0

!" (1)

#

π ∗ ((bi , bj , di = 0, dj = 0, m = 5)|a = 1) !" (2)

#

π ∗ ((bi , bj , di = 1, dj = 1, m = 5)|a = 1) !" (3)

#

π ∗ ((bi , bj , di = 1, dj = 0, m = 5)|a = 1), !" (4)

(11.59)

#

where •

• •

•

(1) is for the case in which mobile node i does not consume the energy from its battery, and mobile node j can also receive energy from mobile node i as mobile node j is consuming one unit of energy (i.e., dj = 1), (2) is for the case similar to (1) but without energy consumption by any mobile node, (3) is for the case in which mobile node i consumes the energy from its battery, and mobile node j can also receive energy from mobile node i as mobile node j is consuming one unit of energy, and (4) is for the case similar to (3) except that mobile node j does not consume energy.

A similar expression can be derived for the average amount of energy transferred from mobile node j to mobile node i. Without matching between mobile nodes i and j, a fixed policy is applied, which is defined as follows:  1, a = 0, (11.60) π † (ω|a) = 0, otherwise, where no energy transfer is allowed. Mobile nodes always take the action a = 0. Now, we obtain the steady state probability of the mobile nodes without matching. The probability is denoted by ψ(ω), the vector of which is denoted by ψ. This vector is obtained by solving ψ  P(a = 0) = ψ  and ψ  1 = 1, where 1 is a vector of ones with an appropriate size. From the steady state probability, we can obtain the individual energy outage probability of the mobile nodes without matching from 10 Mar 2017 at 08:08:03, .012

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Li =

Bj 1  5  

ψ((bi = 0, bj , di = 1, dj , m)),

(11.61)

ψ((bi , bj = 0, di , dj = 1, m)).

(11.62)

bj =0 dj =0 m=1

Lj =

Bi  1  5  bi =0 di =0 m=1

This individual energy outage probabilities without matching are used in the first and second conditions of (11.55) to ensure that none of the mobile nodes is worse off as a result the matching.

11.5.3

Matching among Mobile Nodes Mobile nodes can evaluate the benefits from matching with each other through an optimal energy sharing policy obtained from the CMDP. In this case, they can find the best node to match with in order that their energy outage probability is minimized. Alternatively, they may choose not to match with any node if doing so cannot improve the energy outage probability performance. Again, N denotes the set of all mobile nodes in the network that seek matching. The set can be partitioned into subsets of pairs of mobile nodes or a singleton situation, in which one mobile node acts alone. We first define the preference of the mobile node i ∈ N as i for any node j or k where j, k ∈ N \ {i}. We define j i k as denoting that mobile node i prefers to match with mobile node j rather than with mobile node k. For example, matching mobile node i with node j yields a lower energy outage probability for node i than does matching node i with node k. Here, the preference is not reciprocal insofar as node j may not receive a lower energy outage probability from matching with node i. In general, the preference is assumed to have the following properties [47]. • • •

Antisymmetry. For all i ∈ N , j i k and k i j if and only if j = k. Transitivity. If j i k and l i j, then l i k. Totality. j i k or k i j.

We define a preference profile as a set of preferences of all mobile nodes for all other mobile nodes in N . The preference profile is denoted by  = (i )i∈N . A matching structure is a set of pairs that contain all of the mobile nodes, including singletons. In particular, it is a partitioning of N . We also define j = (i) as denoting that mobile node j is matched with mobile node i to share energy. (i) is called a mate or friend of mobile node i. If (i) = i, then it is called a singleton. A matching structure  is blocked by a pair {i, j} ⊆ N if j i k = (i) and i j l = (j). In this case, mobile node i prefers mobile node j over its current matched mobile node k, and mobile node j also prefers mobile node i over its current matched mobile node l. Thus, mobile nodes i and j will deviate from their current matchings and will match with each other. If {i, j} blocks , then {i, j} is called a blocking pair for . A pair {i, j} ⊆ N that is not a blocking pair for  is called a non-blocking pair for . 10 Mar 2017 at 08:08:03, .012

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The mobile nodes are individually rational in that there must be no blocking pair {i, j} with i = j. Thus, a matching structure is stable if there is no blocking pair. Let S() be a set of individually rational matchings for the preference profile  with a set of mobile nodes N . Then, the set of stable matchings is S ∗ (). The matching preference profile is solvable if S ∗ () = ∅. To obtain a stable matching structure, a linear programming model can be formulated as follows [48]:  min Oi (j)x(i,j) , x(i,j)

subject to

i∈N



x(i,j) = 1,

j∈N



k:k≺j i

x(k,j) +

∀i,



x(i,k) + x(i,j) ≤ 1, ∀i, j ∈ N ,

(11.63)

k:k≺i j

where Oi (j) represents the individual energy outage probability of mobile node i when it matches with mobile node j. This probability is obtained as in (11.57). The decision variable of the linear programming model is x(i,j) . It has a value of one if mobile nodes i and j are matched, and is zero otherwise. • •

The objective function in the top line of (11.63) is chosen to minimize the total energy outage probability. The second constraint in (11.63) guarantees that mobile node j will not match with another mobile node k that results in a higher energy outage probability than that which would be obtained if it matched with mobile node i. Similarly, mobile node i will not match with another mobile node k that results in a higher energy outage probability than that which would be obtained if it matched with mobile node j. In particular, {i, j} must not be a blocking pair.

With two mobile nodes 1 and 2 matched with each other, the optimal energy sharing policy is shown in Figure 11.16. The two mobile nodes have an identical energy charging rate and energy consumption rate. The maximum capacity of the battery is 10 units of energy. Figures 11.16(a), (b), and (c) show the probabilities of taking actions “user 1 transfers energy to user 2,” “user 2 transfers energy to user 1,” and “no transfer,” respectively. We observe that one mobile node will transfer energy to another node if that node has a higher energy level in the battery. The mobile nodes will not transfer energy if their energy levels are not too different. However, when mobile node 1 has an energy charging rate smaller than that of mobile node 2, the optimal energy sharing policy is affected (Figure 11.17). Basically, mobile node 1 will transfer energy to mobile node 2 less frequently (Figure 11.17(c)). In this case, only when the energy level of mobile node 1 is much larger than that of mobile node 2 will mobile node 1 transfer energy. The energy charging rates and energy consumption rates of 20 users were varied, and Figure 11.18 shows a matching among them. Stable matching happens between mobile nodes with similar amounts of residual energy, i.e., energy charging minus 10 Mar 2017 at 08:08:03, .012

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Mobile node 1 transfers to mobile node 2

(a)

1 0.8 0.6 0.4 0.2 0 0 2 10

4

8

6

6 4

8 10

Mobile node 1

2 0

Mobile node 2

Mobile node 2 transfers to mobile node 1

(b)

1 0.8 0.6 0.4 0.2 0 0 2 10

4

8

6

6 4

8 10

Mobile node 1

2 0

Mobile node 2

(c)

1 0.8 Do nothing

422

0.6 0.4 0.2 0 0 2 10

4

8

6

6 4

8 Mobile node 1

10

2 0

Mobile node 2

Figure 11.16 Energy sharing policy (symmetric case, where users 1 and 2 have the same energy

charging rate). 10 Mar 2017 at 08:08:03, .012

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Mobile node 1 transfers to mobile node 2

(a)

1 0.8 0.6 0.4 0.2 0 0 2 10

4

8

6

6 4

8 10

Mobile node 1

2 0

Mobile node 2

Mobile node 2 transfers to mobile node 1

(b)

1 0.8 0.6 0.4 0.2 0 0 2 10

4

8

6

6 4

8 10

Mobile node 1

2 0

Mobile node 2

(c)

1 Do nothing

0.8 0.6 0.4 0.2 0 0 2 10

4

8

6

6 4

8 Mobile node 1

10

2 0

Mobile node 2

Figure 11.17 Energy sharing policy (asymmetric case, where user 1 has a smaller energy charging

rate). 10 Mar 2017 at 08:08:03, .012

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0.12 24

10 0.115

Energy consumption rate

12 0.11

8

2

17

22 20 21

23

6 18 0.105

16

3 19 5

0.1

14

11 0.095

4

9

7

1

13

15 0.09 0.11

0.115

0.12

0.125

0.13

0.135

0.14

0.145

0.15

Energy charging rate Figure 11.18 Matching of 20 users.

energy consumption. For example, a node with a high energy charging rate and a high energy consumption rate tends to match with a node with a low energy charging rate and a low energy consumption rate. When mobile nodes have similar amounts of residual energy, they will not exploit each other, but will complement one another’s operations and thus derive mutual benefit.

11.6

Future Research Directions For MANETs and DTNs, the following issues can be studied. •

Equilibrium and competitive energy pricing. While energy can be transferred and exchanged in a mobile environment, a price can be imposed to incentivize energy sources and energy carriers. However, because of random mobility, energy demand and supply have to be quantified, in order to determine the energy prices accordingly. An energy price can be determined on the basis of an energy trading structure and the number of energy sellers and buyers. An equilibrium price can be determined as the price that maximizes the profit of an energy supplier and the utility of an energy consumer. This is the price at which the energy supply equals the demand for energy. Alternatively, if there are multiple energy sellers in the network, they have to compete on price in order attract more buyers. Noncooperative game theory can be applied to analyze and obtain the competitive 10 Mar 2017 at 08:08:03, .012

Mobile Ad-Hoc Networks and Delay-Tolerant Networks

•

•

•

11.7

425

energy prices offered to the energy consumers. A Nash equilibrium solution for pricing can be adopted. Energy auction. In a mobile environment, the energy supply can be limited and multiple energy consumers may compete to obtain energy. An auction mechanism can be applied to the energy supplier to maximize its profit. There are two major types of auction that can be applied, i.e., single-sided and double-sided auctions. In a single-sided auction, there is only one seller or one buyer. In a double-sided auction, there are multiple sellers and buyers. In the auction, efficiency of the market is required in order to ensure that the benefits of all participants are maximized. Additionally, the individual rationality and incentive compatibility properties of the auction mechanism have to be evaluated. Individual rationality guarantees that all participants receive non-negative benefit. Incentive compatibility assures that the participants will receive the maximum benefit if they report true information in the auction. Energy contract. Energy suppliers and consumers can arrange a contract for energy delivery. Contract theory can be applied to determine the optimal contract design that maximizes the profit of the energy suppliers while the energy consumers are satisfied with the energy they obtain. Evaluation with real mobility trace. It is important to analyze the performance of energy supply in MANETs and DTNs using real trace data to show that the algorithms are practical. Some examples of trace datasets that are available are RollerNet [49], Cambridge [50], and Haggle, a European Union-funded project in situated and autonomic communications [51].

Summary We have discussed wireless-powered mobile ad-hoc networks (MANETs) and delaytolerant networks (DTNs). MANETs and DTNs are different from fixed networks in that their data transfer is affected by the mobility of the nodes and users. In DTNs, endto-end paths from sources to destinations may not be available, so mobile nodes have to carry and store content until they can forward it to other nodes. This introduces challenges for energy replenishment and wireless energy transfer. We have provided a brief introduction to MANETs and DTNs. Then, some energy efficiency issues in MANETs and DTNs were reviewed. Then, we presented three approaches to address wireless energy transfer in MANETs and DTNs. The first approach is based on cooperation among mobile nodes in DTNs. The mobile nodes receive limited amounts of wireless energy from wireless chargers. Thus, they have to make a decision regarding whether to cooperate with each other to deliver contents, which consumes considerable energy, or not. The second approach concerns delay-limited communication in MANETs. A mobile node receives wireless energy and makes a decision regarding whether to transmit its data or not. The energy management and deployment of the wireless chargers have also been considered. The third approach considers mobile energy sharing that allows multiple mobile nodes to transfer energy among themselves in such a way as to 10 Mar 2017 at 08:08:03, .012

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minimize the chance of energy depletion. For all three approaches, optimization models have been described. Finally, we have outlined some potential future research directions.

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Index

AC/DC rectifier, 8 additive white Gaussian noise, 271 Alliance for Wireless Power (A4WP), 7, 21 ambient energy harvesting, 268 amplify-and-forward (AF), 140 amplitude shift keying (ASK), 34 angular coverage, 124 antenna design, 309 antennas horn, 131 aperture, 91, 92, 94, 95, 99 area demonetization, 294 artificial noise, 172, 200, 201

DC–DC converter, 47 decode-and-forward (DF), 140 densification, 265 device-to-device (D2D), 268, 278 dielectric constant, 99 differentiated RF power transmission (DRIFT), 296 dipole antenna, 87, 88, 93 discretization, 301 downlink, 135 downlink energy transmission, 136 downlink information transmission, 135 driver amplifier, 49 dual decomposition technique, 152

backscattering communication systems, 217 beamforming, 292 beamwidth, 94, 96, 122–124 best response, 325 bio-sensors, 44 Bluetooth Low Energy (BLE), 47 body area network, 311

eavesdroppers, 172, 199–201, 203, 207 efficiency, 87, 89–91, 102, 103, 123, 126, 127 collection, 92 conversion, 93, 98 electric induction, 90 energy beamforming, 176 energy cooperation, 141 energy efficiency, 153, 171–173, 175, 191, 209 energy forwarding relay, 143 energy harvesting, 86, 87, 92, 93, 95–97, 100, 103, 113, 123, 126, 127 energy harvesting efficiency, 142 energy harvesting relay, 141 energy harvesting sensor networks, 74 energy management algorithm, 74 energy relaying, 137 energy scheduling, 312 energy signal, 173, 192, 200, 201, 205–207 energy storage unit, 47 energy synchronized charging (ESync), 306 energy transfer efficiency, 172, 193, 199, 205, 208 energy transmitting relay, 145 envelope correlation, 116–118 Europe RFID, 34 European Committee for Electro-technical Standardization (CENELEC), 22 European Committee for Standardization (CEN), 22 European Standards Organizations (ESOs), 22 European Telecommunications Standards Institute (ETSI), 22

cavity model, 98, 99 channel inversion, 275 channel inversion power control, 278 chi-squared distribution, 268 chip antenna, 63 circuit design, 44 circuit-layer stored energy evolution model, 44 co-channel interference (CCI), 265 Comité International Spécial des Perturbations Radioélectriques (CISPR), 22 complementary metal–oxide semiconductor (CMOS), 309 conductive material, 8 constrained Nash equilibrium, 324 constrained stochastic game, 322 Cota, 44 coupling co-efficiency, 311 coupling manipulation, 311 coverage probability, 283 cross-layer design, 44 cumulative distribution function, 271 cyclic prefix, 270

430 Downloaded from https:/www.cambridge.org/core. Columbia University Libraries, on 12 Jun 2017 at 22:32:46, subject to the Cambridge Core terms of use, available at

Index

far-field based RF energy transfer, 44 far-field energy harvesting, 4 Federal Communications Commission (FCC), 16 femtocell, 273 free-positioning with coil array, 25 frequency matching, 311 Friis equation, 45, 91, 92 fringing field, 98, 99 full-duplex, 164 gamma distribution, 271 Ginibre-determinantal point process (DPP), 270 grating lobe, 95, 113 greedy cone selecting (NB-GCS), 292 greedy time-switching protocol, 142 green communication, 3 ground-based transmission, 91 GSM, 34 half-duplex, 140 harvest-then-transmit, 274 helical antenna, 95 high-power/long-range test-bed, 45 horn antenna, 95 Hungarian method, 152 IEEE P2100.1, 29 impedance matching, 310, 311 impedance matching circuit, 14 imperfect CSI, 172, 188 incremental effective coverage (IEC), 307 inductive coupling, 90 Industrial Scientific Medical (ISM), 26 interference, 109, 115 interference management, 166 International Electrotechnical Commissions (IEC), 22 Internet of Things (IoT), 329 joint periodic wake-up (JPW), 302 k-means clustering, 302 knapsack, 294 Lagrangian, 155 landmark provisioning, 292 leakage current, 81 Lévy distribution, 278 Li-ion battery, 47 linear programming (LP), 301 linearization, 301 low-power/short-range test-bed, 45 machine-to-machine communication (M2M), 329 MagMIMO, 31 magnetic field intensity, 310 magnetic induction, 89, 90

431

magnetic inductive coupling, 8 magnetic resonance coupling, 10 Markov chain, 271, 276, 282 Markov decision process (MDP), 312 massive MIMO, 87, 95, 100, 103, 123, 126, 127 matching circuit, 27, 47 matching network, 49, 310 matrix inversion, 277 microcontroller unit (MCU), 5 microstrip, 96–100, 109, 113, 123, 124, 127 conventional, 112, 113 slotted, 97, 98, 103, 104, 106, 114, 127 U-slot, 109, 110, 112, 113 microwave power transmission (MPT), 86, 88, 89 mixed integer linear programming (MILP), 293 mobile ad-hoc networks (MANETs), 383 mobile charger dispatch, 291 mobility-aware charger deployment (MACD), 295 multi-hop energy transfer, 143 multi-objective optimization, 173, 190, 191, 193, 209 multi-path energy routing, 145 multi-tier cellular network, 266 multihop provisioning, 292 multiple-input multiple-output, 87, 170 mutual inductance, 311 narrowband, 93, 97, 103, 105 near-field energy transfer, 4 Nikola Tesla, 6 node pair based greedy cone selecting (PB-GCS), 292 non-convex optimization, 180, 186, 203, 209 non-deterministic arrival, 286 NS-2, 303 OFDMA, 148 optimal time allocation, 153 optimization, 154 ordinary differential equation (ODE), 81 particle swarm optimization (PSO), 303 path loss, 46 path provisioning, 292 pattern antenna, 49 perfect CSI, 175, 185, 188, 202 perfect electric conductor (PEC), 99 perfect magnetic conductor (PMC), 99 phase progression, 123 phased array, 88, 95, 96, 124 photovoltaic technology, 3 physical layer security, 209 piezoelectric effect, 4 point provisioning, 292 points of interest (PoI), 302 Poisson point process, 268

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432

Index

polarization circular, 113, 123 cross, 102, 105, 106, 109 diversity, 87, 109, 110, 114, 115, 121, 127 dual, 110, 112, 113 linear, 105, 115, 123 power allocation, 151 power amplifier, 49, 278 power beacon, 249 power conversion, 27 power delivery far-field, 91 near-field, 90 power efficient, 179, 185, 206, 208 power management unit (PMU), 4 Power Matters Alliance (Powermat), 7, 21 power receiving unit (PRU), 26 power splitter, 49 power splitting ratio, 172, 183, 210 power splitting receivers, 172, 176, 179 power transmitter unit (PTU), 26 power-splitting protocol, 142 Powercast, 33, 44 Powerharvester, 35 probability density function, 271 Qi, 21 QoS, 170–172, 175, 189, 194, 200 quality of monitoring (QoM), 302 quasi-Yagi antenna, 52 radiation patterns, 95, 102, 105, 106, 110, 112, 113, 116, 119, 121, 123, 127 omni-directional, 93 pencil-beam, 94 radio-frequency identification (RFID), 9 random walk, 276 rank-one matrix, 177, 181, 183, 210 Rayleigh block fading, 271 Rayleigh fading, 282 receiver antenna gain, 45 receiver sensitivity, 44, 281 rectenna, 14, 88, 89, 91, 93 rectifier, 88, 89, 91–93, 310 rectifying efficiency, 310 reflector antenna, 88, 93–95 relay, 136 relay operation policy, 139 relay selection, 151 resonator, 27 resource allocation, 147 RF energy harvesting network, 267 RF power beacon, 45 RF-to-DC conversion circuit, 46 RF-to-DC conversion efficiency, 273 RF-to-DC power converter, 49 RF-to-DC rectification, 310

RFID, 294 robust beamforming, 186, 188, 209 Schottky diode, 47 SDP relaxation, 181, 182, 187, 188, 194, 196, 203, 204, 209 secondary network, 268 secrecy rate, 172, 202, 205, 207 secure SWIPT, 172, 200 Seebeck effect, 3 self-inductance, 311 self-interference, 164 semidefinite programming, 180 sensor network, 291 separated receivers, 176, 186, 191, 200 set-cover-based approach, 302 Sheskin algorithm, 277 shortest Hamiltonian cycle (SHC), 295, 300 signal-to-interference ratio, 271 simultaneous wireless information and power transfer (SWIPT), 15 slot antenna, 110, 114 small cell base station, 265 small cell network, 265 Society of Automotive Engineers (SAE), 29 spark-excited radio-frequency resonant transformer, 6 spatial density, 283, 284 static wireless charger deployment, 291 steady state probability, 277 stored energy evolution model, 76 subcarrier assignment, 151 supercapacitor, 35, 44 superposition property, 275 SuReSense, 295 SWIPT, 137 test-beds, 44 thermal energy, 3 thermoelectric, 3 Thomson effect, 3 throughput performance, 155 time and power allocation, 154 time-switching-based protocol for energy harvesting, 141 trail covering utility (TCU), 307 transmission-line model, 98 transmitter antenna gain, 45 transverse magnetic (TM) mode, 97, 99 traveling salesman problem (TSP), 300 true wireless, 91 U-slot patch, 112, 113 ultra-high frequency (UHF), 87, 90 ultra-wideband (UWB), 110, 114 universal software radio peripheral (USRP), 76

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Index

uplink information transmission, 135 upper-layer energy management algorithm, 44 vector signal generator, 52 vibration, 4 Vivaldi antenna, 110, 114 voltage multiplier, 14 VSWR, 104 Wardenclyffe Tower, 6 wideband, 87, 94, 95, 97, 103, 109, 110, 114, 127 wideband diversity antennas, 109 wireless charging, 44

433

wireless identification and sensing platform (WISP), 294 Wireless Power Consortium (WPC), 7, 21 wireless power transfer, 135 wireless-powered sensor network, 291, 312 wireless sensor network, 278 wireless-powered cellular network (WPCN), 246 wireless-powered communication, 137 wireless-powered communication network architecture, 17 wireless-powered cooperative communication, 137 WiTricity, 6

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